Operator algebras: theory of C*-algebras and von Neumann algebras
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg
Springer
[2006]
|
| Schriftenreihe: | Encyclopaedia of mathematical sciences
volume 122 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xx, 517 Seiten |
| ISBN: | 3540284869 9783540284864 9783642066733 |
Internformat
MARC
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|---|---|---|---|
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| 020 | |a 9783540284864 |q hardcover |9 978-3-540-28486-4 | ||
| 020 | |a 9783642066733 |q softcover |9 978-3-642-06673-3 | ||
| 035 | |a (OCoLC)181481200 | ||
| 035 | |a (DE-599)BVBBV021268155 | ||
| 040 | |a DE-604 |b ger |e rda | ||
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| 049 | |a DE-19 |a DE-824 |a DE-355 |a DE-91G |a DE-29T |a DE-634 |a DE-11 |a DE-188 |a DE-20 |a DE-83 | ||
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| 084 | |a MAT 467f |2 stub | ||
| 084 | |a 46L05 |2 msc | ||
| 100 | 1 | |a Blackadar, Bruce |d 1948- |e Verfasser |0 (DE-588)111248485 |4 aut | |
| 245 | 1 | 0 | |a Operator algebras |b theory of C*-algebras and von Neumann algebras |c B. Blackadar |
| 264 | 1 | |a Berlin ; Heidelberg |b Springer |c [2006] | |
| 264 | 4 | |c © 2006 | |
| 300 | |a xx, 517 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Encyclopaedia of mathematical sciences / Operator algebras and non-commutative geometry |v 3 | |
| 490 | 1 | |a Encyclopaedia of mathematical sciences |v volume 122 | |
| 650 | 4 | |a C*-algebras | |
| 650 | 4 | |a Von Neumann algebras | |
| 650 | 0 | 7 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a VonNeumann-Algebra |0 (DE-588)4388395-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a C-Stern-Algebra |0 (DE-588)4136693-1 |D s |
| 689 | 0 | 1 | |a Operatortheorie |0 (DE-588)4075665-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a VonNeumann-Algebra |0 (DE-588)4388395-3 |D s |
| 689 | 1 | 1 | |a Operatortheorie |0 (DE-588)4075665-8 |D s |
| 689 | 1 | |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-540-28517-5 |
| 810 | 2 | |a Operator algebras and non-commutative geometry |t Encyclopaedia of mathematical sciences |v 3 |w (DE-604)BV014111511 |9 3 | |
| 830 | 0 | |a Encyclopaedia of mathematical sciences |v volume 122 |w (DE-604)BV024126459 |9 122 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014589313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-014589313 | ||
Datensatz im Suchindex
| _version_ | 1804135046767968256 |
|---|---|
| adam_text | Contents
I
Operators
on
Hubert Space................................ 1
1.1 Hubert Space......................................... 1
1.1.1 Inner Products............................... 1
1.1.2
Orthogonality
............................... 2
1.1.3 Dual Spaces
and Weak Topology
...............
З
1.1.4 Standard
Constructions
....................... 4
1.1.5
Real Hubert Spaces
.......................... 5
1.2
Bounded Operators
.................................... 5
1.2.1
Bounded Operators on Normed Spaces
.......... 5
1.2.2
Sesquilinear Forms
........................... 6
1.2.3
Adjoint
..................................... 7
1.2.4
Self-Adjoint, Unitary, and Normal Operators
.... 8
1.2.5
Amplifications and
Commutants
............... 9
1.2.6
Invertibility and Spectrum
.................... 10
1.3
Other Topologies on
ЦП)
.............................. 13
1.3.1
Strong and Weak Topologies
................... 13
1.3.2
Properties of the Topologies
................... 14
1.4
Functional Calculus
.................................... 17
1.4.1
Functional Calculus for Continuous Functions
.... 18
1.4.2
Square Roots of Positive Operators
............. 19
1.4.3
Functional Calculus for
Borei
Functions
......... 19
1.5
Projections
........................................... 19
1.5.1
Definitions and Basic Properties
............... 20
1.5.2
Support Projections and Polar Decomposition
... 21
1.6
The Spectral Theorem
................................. 23
1.6.1
Spectral Theorem for Bounded Self-Adjoint-
Operators
................................... 23
1.6.2
Spectral Theorem for Normal Operators
........ 25
1.7
Unbounded Operators
.................................. 27
1.7.1
Densely Defined Operators
.................... 27
1.7.2
Closed Operators and
Adjoints
................. 29
XVI Contents
1.7.3
Self-Adjoint Operators
........................ 30
1.7.4
The Spectral Theorem and Functional Calculus
for Unbounded Self-Adjoint Operators
.......... 32
1.8
Compact Operators
.................................... 36
1.8.1
Definitions and Basic Properties
............... 36
1.8.2
The Calkin Algebra
.......................... 37
1.8.3
Predholm Theory
............................ 37
1.8.4
Spectral Properties of Compact Operators
....... 40
1.8.5
Trace-Class and Hilbert-Schmidt Operators
...... 41
1.8.6
Duals and Preduals,
σ-
Topologies
.............. 43
1.8.7
Ideals of £(H)
............................... 44
1.9
Algebras of Operators
.................................. 47
1.9.1
Commutant
and Bicommutant
................. 47
1.9.2
Other Properties
............................. 48
II C*-Algebras
............................................... 51
11.
1
Definitions and Elementary Facts
........................ 51
11.
1.1
Basic Definitions
............................. 51
11.1.2 Unitization
.................................. 53
II.
1.3
Power series, Inverses, and Holomorphic Functions
54
II.
1.4
Spectrum
................................... 54
II.
1.5
Holomorphic Functional Calculus
.............. 55
II.
1.6
Norm and Spectrum
.......................... 57
11.
2
Commutative C*-Algebras and Continuous Functional
Calculus
.............................................. 59
11.
2.1
Spectrum of a Commutative Banach Algebra
.... 59
11.2.2 Gelfand Transform
........................... 60
11.2.3 Continuous Functional Calculus
................ 61
11.3
Positivity,
Order, and Comparison Theory
................ 63
11.3.1 Positive Elements
............................ 63
11.3.2 Polar Decomposition
......................... 67
11.
3.3
Comparison Theory for Projections
............. 72
11.3.4 Hereditary C*-Subalgebras and General
Comparison Theory
.......................... 75
11.4 Approximate Units
.................................... 79
II.4.1 General Approximate Units
................... 79
Π.4.2
Strictly Positive Elements and
σ
-Unital
C*-Algebras
................................. 81
Π.4.3
Quasicentral Approximate Units
............... 82
11.5 Ideals, Quotients, and Homomorphisms
.................. 82
11.5.1 Closed Ideals
................................ 83
11.5.2 Nonclosed Ideals
............................. 85
11.5.3 Left Ideals and Hereditary Subalgebras
......... 89
Π.5.4
Prime and Simple C*-Algebras
................. 93
11.5.5 Homomorphisms and Automorphisms
........... 95
Contents XVII
11.6 States
and Representations
.............................100
11.
6.1
Representations
..............................101
11.6.2 Positive Linear Functionate and States
..........103
11.
6.3
Extension and Existence of States
..............106
11.6.4 The GNS Construction
.......................107
11.6.5 Primitive Ideal Space and Spectrum
............
Ill
11.6.6 Matrix Algebras and Stable Algebras
...........116
11.6.7 Weights
.....................................118
11.6.8 Traces and Dimension Functions
...............121
И.6.9
Completely Positive Maps
.....................124
II.
6.10
Conditional Expectations
.....................132
11.7 Hubert Modules, Multiplier Algebras, and Morita Equivalence^
11.7.1
Hubert Modules
.............................137
11.7.2 Operators
...................................141
11.7.3 Multiplier Algebras
...........................144
11.7.4 Tensor Products of Hubert Modules
............147
II.
7.5
The Generalized Stinespring Theorem
..........149
II.
7.6
Morita Equivalence
...........................150
11.
8
Examples and Constructions
............................154
11.8.1 Direct Sums, Products, and Ultraproducts
......154
11.8.2 Inductive Limits
.............................156
11.8.3 Universal C^Algebras and Free Products
.......158
11.8.4 Extensions and Pullbacks
.....................167
11.8.5 C^-Algebras with Prescribed Properties
.........176
11.9 Tensor Products and Nuclearity
.........................179
II.9.1 Algebraic and Spatial Tensor Products
..........180
П.9.2
The Maximal Tensor Product
..................180
11.9.3 States on Tensor Products
.....................182
11.9.4 Nuclear C*-Algebras
..........................184
П.9.5
Minimality of the Spatial Norm
................186
11.9.6 Homomorphisms and Ideals
...................187
11.9.7 Tensor Products of Completely Positive Maps
... 190
11.9.8 Infinite Tensor Products
......................191
11.10
Group C*-Algebras and Crossed Products
................192
11.10.1
Locally Compact Groups
......................193
11.10.2 Group ^-Algebras
...........................197
11.10.3 Crossed products
.............................199
11.10.4 Transformation Group C*-Algebras
.............205
11.10.5 Takai Duality
................................211
II.
10.6
Structure of Crossed Products
.................212
II.10.7 Generalizations of Crossed Product Algebras
.... 212
II.
10.8
Duality and Quantum Groups
.................214
XVIII
Contents
III Von
Neumann Algebras
...................................221
ULI
Projections and Type Classification
......................222
III.
1.1
Projections and Equivalence
...................222
111.
1.2
Cyclic and Countably Decomposable Projections
. 225
111.
1.3
Finite, Infinite, and Abelian Projections
.........227
III.
1.4
Type Classification
...........................231
111.
1.5
Tensor Products and Type I
von
Neumann
Algebras
....................................232
III.
1.6
Direct Integral Decompositions
................237
111.
1.7
Dimension Functions and Comparison Theory
.. . 240
111.1.8 Algebraic Versions
...........................243
111.
2
Normal Linear Functionals and Spatial Theory
............244
111.2.1 Normal and Completely Additive States
.........245
111.
2.2
Normal Maps and Isomorphisms
of
von
Neumann Algebras
.....................248
111.2.3 Polar Decomposition for Normal Linear
Functionals and the Radon-Nikodym Theorem
. . . 257
111.
2.4
Uniqueness of the Predual and Characterizations
of W*- Algebras
..............................259
ΙΠ.2.5
Traces on
von
Neumann Algebras
..............260
111.2.6 Spatial Isomorphisms and Standard Forms
......269
111.3 Examples and Constructions of Factors
...................275
ΠΙ.3.1
Infinite Tensor Products
......................275
III.3.2 Crossed Products and the Group Measure
Space Construction
...........................280
ΙΠ.3.3
Regular Representations of Discrete Groups
.....288
III.3.4 Uniqueness of the Hyperfinite
Πι
Factor
........291
111.4 Modular Theory
.......................................293
ΙΠ.4.1
Notation and Basic Constructions
..............293
111.4.2 Approach using Bounded Operators
............295
111.4.3 The Main Theorem
...........................295
111.4.4 Left Hilbert Algebras
.........................296
111.4.5 Corollaries of the Main Theorems
..............299
111.4.6 The Canonical Group of Outer Automorphisms
and Connes Invariants
........................302
111.4.7 The KMS Condition and the Radon-Nikodym
Theorem for Weights
.........................306
111.4.8 The Continuous and Discrete Decompositions
of a
von
Neumann Algebra
....................310
HI.4.8.1 The Flow of Weights
..................312
111.5 Applications to Representation Theory of C*-Algebras
.....313
111.5.1
Decomposition Theory for Representations
......313
111.5.2 The Universal Representation and Second Dual
.. 318
Contents XIX
IV Further Structure
.........................................323
IV.l Type I C*-Algebras
....................................323
IV.1.1 First Definitions
.............................323
IV.1.2 Elementary
C*-Algebras
......................326
IV.
1.3
Liminal and Postliminal C*-Algebras
...........327
IV.
1.4
Continuous Trace, Homogeneous,
and Subhomogeneous C*-Algebras
..............329
IV.
1.5
Characterization of Type I C*-
Algebr
as
.........337
IV.1.6 Continuous Fields of C*-Algebras
..............340
IV.
1.7
Structure of Continuous Trace C*-Algebras
......344
IV.2 Classification of Injective Factors
........................350
IV.2.1 Injective C*-Algebras
.........................352
IV.2.2 Injective
von
Neumann Algebras
...............353
IV.2.3 Normal Cross Norms
..........................360
IV.2.4
Semidiscrete
Factors
..........................362
IV.2.
5
Amenable
von
Neumann Algebras
..............365
IV.2.6 Approximate Finite Dimensionality
.............367
IV.2.
7
Invariants and the Classification of Injective
Factors
.....................................367
IV.3 Nuclear and Exact C*-Algebras
.........................368
IV.3.1 Nuclear C*-Algebras
..........................368
IV.3.2 Completely Positive Liftings
...................374
IV.3.3 Amenability for C*-Algebras
...................378
IV.
3.4
Exactness and Subnuclearity
...................383
IV.3.5 Group C^Algebras and Crossed Products
.......391
V K-Theory and Finiteness
..................................395
V.I K-Theory for C^Algebras
..............................395
V.I.I KO-Theory
..................................396
V.l.2
Κχ
-Theoľy
and Exact Sequences
...............402
V.1.3 Further Topics
...............................408
V.1.4 Bivariant Theories
...........................411
V.l.5
Axiomatic it-Theory and the Universal
Coefficient. Theorem
..........................413
V.2 Finiteness
............................................418
V.2.1 Finite and Properly Infinite
Unital C*-
Algebras
.. 418
V.2.2 Nonunital C*-Algebras
........................423
V.2.3 Finiteness in Simple C*-Algebras
...............430
V.2.4 Ordered Ji-Theory
...........................434
V.3 Stable Rank and Real Rank
............................444
V.3.1 Stable Rank
.................................445
V.3.2 Real Rank
..................................452
V.4 Quasidiagonality
......................................457
V.4.1
Quasidiagonal
Sets of Operators
...............457
V.4.2
Quasidiagonal
С*-
Algebras
....................460
XX
Contents
V.4.3
Generalized Inductive
Limits ..................464
References
.....................................................479
Index..........................................................505
|
| adam_txt |
Contents
I
Operators
on
Hubert Space. 1
1.1 Hubert Space. 1
1.1.1 Inner Products. 1
1.1.2
Orthogonality
. 2
1.1.3 Dual Spaces
and Weak Topology
.
З
1.1.4 Standard
Constructions
. 4
1.1.5
Real Hubert Spaces
. 5
1.2
Bounded Operators
. 5
1.2.1
Bounded Operators on Normed Spaces
. 5
1.2.2
Sesquilinear Forms
. 6
1.2.3
Adjoint
. 7
1.2.4
Self-Adjoint, Unitary, and Normal Operators
. 8
1.2.5
Amplifications and
Commutants
. 9
1.2.6
Invertibility and Spectrum
. 10
1.3
Other Topologies on
ЦП)
. 13
1.3.1
Strong and Weak Topologies
. 13
1.3.2
Properties of the Topologies
. 14
1.4
Functional Calculus
. 17
1.4.1
Functional Calculus for Continuous Functions
. 18
1.4.2
Square Roots of Positive Operators
. 19
1.4.3
Functional Calculus for
Borei
Functions
. 19
1.5
Projections
. 19
1.5.1
Definitions and Basic Properties
. 20
1.5.2
Support Projections and Polar Decomposition
. 21
1.6
The Spectral Theorem
. 23
1.6.1
Spectral Theorem for Bounded Self-Adjoint-
Operators
. 23
1.6.2
Spectral Theorem for Normal Operators
. 25
1.7
Unbounded Operators
. 27
1.7.1
Densely Defined Operators
. 27
1.7.2
Closed Operators and
Adjoints
. 29
XVI Contents
1.7.3
Self-Adjoint Operators
. 30
1.7.4
The Spectral Theorem and Functional Calculus
for Unbounded Self-Adjoint Operators
. 32
1.8
Compact Operators
. 36
1.8.1
Definitions and Basic Properties
. 36
1.8.2
The Calkin Algebra
. 37
1.8.3
Predholm Theory
. 37
1.8.4
Spectral Properties of Compact Operators
. 40
1.8.5
Trace-Class and Hilbert-Schmidt Operators
. 41
1.8.6
Duals and Preduals,
σ-
Topologies
. 43
1.8.7
Ideals of £(H)
. 44
1.9
Algebras of Operators
. 47
1.9.1
Commutant
and Bicommutant
. 47
1.9.2
Other Properties
. 48
II C*-Algebras
. 51
11.
1
Definitions and Elementary Facts
. 51
11.
1.1
Basic Definitions
. 51
11.1.2 Unitization
. 53
II.
1.3
Power series, Inverses, and Holomorphic Functions
54
II.
1.4
Spectrum
. 54
II.
1.5
Holomorphic Functional Calculus
. 55
II.
1.6
Norm and Spectrum
. 57
11.
2
Commutative C*-Algebras and Continuous Functional
Calculus
. 59
11.
2.1
Spectrum of a Commutative Banach Algebra
. 59
11.2.2 Gelfand Transform
. 60
11.2.3 Continuous Functional Calculus
. 61
11.3
Positivity,
Order, and Comparison Theory
. 63
11.3.1 Positive Elements
. 63
11.3.2 Polar Decomposition
. 67
11.
3.3
Comparison Theory for Projections
. 72
11.3.4 Hereditary C*-Subalgebras and General
Comparison Theory
. 75
11.4 Approximate Units
. 79
II.4.1 General Approximate Units
. 79
Π.4.2
Strictly Positive Elements and
σ
-Unital
C*-Algebras
. 81
Π.4.3
Quasicentral Approximate Units
. 82
11.5 Ideals, Quotients, and Homomorphisms
. 82
11.5.1 Closed Ideals
. 83
11.5.2 Nonclosed Ideals
. 85
11.5.3 Left Ideals and Hereditary Subalgebras
. 89
Π.5.4
Prime and Simple C*-Algebras
. 93
11.5.5 Homomorphisms and Automorphisms
. 95
Contents XVII
11.6 States
and Representations
.100
11.
6.1
Representations
.101
11.6.2 Positive Linear Functionate and States
.103
11.
6.3
Extension and Existence of States
.106
11.6.4 The GNS Construction
.107
11.6.5 Primitive Ideal Space and Spectrum
.
Ill
11.6.6 Matrix Algebras and Stable Algebras
.116
11.6.7 Weights
.118
11.6.8 Traces and Dimension Functions
.121
И.6.9
Completely Positive Maps
.124
II.
6.10
Conditional Expectations
.132
11.7 Hubert Modules, Multiplier Algebras, and Morita Equivalence^
11.7.1
Hubert Modules
.137
11.7.2 Operators
.141
11.7.3 Multiplier Algebras
.144
11.7.4 Tensor Products of Hubert Modules
.147
II.
7.5
The Generalized Stinespring Theorem
.149
II.
7.6
Morita Equivalence
.150
11.
8
Examples and Constructions
.154
11.8.1 Direct Sums, Products, and Ultraproducts
.154
11.8.2 Inductive Limits
.156
11.8.3 Universal C^Algebras and Free Products
.158
11.8.4 Extensions and Pullbacks
.167
11.8.5 C^-Algebras with Prescribed Properties
.176
11.9 Tensor Products and Nuclearity
.179
II.9.1 Algebraic and Spatial Tensor Products
.180
П.9.2
The Maximal Tensor Product
.180
11.9.3 States on Tensor Products
.182
11.9.4 Nuclear C*-Algebras
.184
П.9.5
Minimality of the Spatial Norm
.186
11.9.6 Homomorphisms and Ideals
.187
11.9.7 Tensor Products of Completely Positive Maps
. 190
11.9.8 Infinite Tensor Products
.191
11.10
Group C*-Algebras and Crossed Products
.192
11.10.1
Locally Compact Groups
.193
11.10.2 Group ^-Algebras
.197
11.10.3 Crossed products
.199
11.10.4 Transformation Group C*-Algebras
.205
11.10.5 Takai Duality
.211
II.
10.6
Structure of Crossed Products
.212
II.10.7 Generalizations of Crossed Product Algebras
. 212
II.
10.8
Duality and Quantum Groups
.214
XVIII
Contents
III Von
Neumann Algebras
.221
ULI
Projections and Type Classification
.222
III.
1.1
Projections and Equivalence
.222
111.
1.2
Cyclic and Countably Decomposable Projections
. 225
111.
1.3
Finite, Infinite, and Abelian Projections
.227
III.
1.4
Type Classification
.231
111.
1.5
Tensor Products and Type I
von
Neumann
Algebras
.232
III.
1.6
Direct Integral Decompositions
.237
111.
1.7
Dimension Functions and Comparison Theory
. . 240
111.1.8 Algebraic Versions
.243
111.
2
Normal Linear Functionals and Spatial Theory
.244
111.2.1 Normal and Completely Additive States
.245
111.
2.2
Normal Maps and Isomorphisms
of
von
Neumann Algebras
.248
111.2.3 Polar Decomposition for Normal Linear
Functionals and the Radon-Nikodym Theorem
. . . 257
111.
2.4
Uniqueness of the Predual and Characterizations
of W*- Algebras
.259
ΙΠ.2.5
Traces on
von
Neumann Algebras
.260
111.2.6 Spatial Isomorphisms and Standard Forms
.269
111.3 Examples and Constructions of Factors
.275
ΠΙ.3.1
Infinite Tensor Products
.275
III.3.2 Crossed Products and the Group Measure
Space Construction
.280
ΙΠ.3.3
Regular Representations of Discrete Groups
.288
III.3.4 Uniqueness of the Hyperfinite
Πι
Factor
.291
111.4 Modular Theory
.293
ΙΠ.4.1
Notation and Basic Constructions
.293
111.4.2 Approach using Bounded Operators
.295
111.4.3 The Main Theorem
.295
111.4.4 Left Hilbert Algebras
.296
111.4.5 Corollaries of the Main Theorems
.299
111.4.6 The Canonical Group of Outer Automorphisms
and Connes' Invariants
.302
111.4.7 The KMS Condition and the Radon-Nikodym
Theorem for Weights
.306
111.4.8 The Continuous and Discrete Decompositions
of a
von
Neumann Algebra
.310
HI.4.8.1 The Flow of Weights
.312
111.5 Applications to Representation Theory of C*-Algebras
.313
111.5.1
Decomposition Theory for Representations
.313
111.5.2 The Universal Representation and Second Dual
. 318
Contents XIX
IV Further Structure
.323
IV.l Type I C*-Algebras
.323
IV.1.1 First Definitions
.323
IV.1.2 Elementary
C*-Algebras
.326
IV.
1.3
Liminal and Postliminal C*-Algebras
.327
IV.
1.4
Continuous Trace, Homogeneous,
and Subhomogeneous C*-Algebras
.329
IV.
1.5
Characterization of Type I C*-
Algebr
as
.337
IV.1.6 Continuous Fields of C*-Algebras
.340
IV.
1.7
Structure of Continuous Trace C*-Algebras
.344
IV.2 Classification of Injective Factors
.350
IV.2.1 Injective C*-Algebras
.352
IV.2.2 Injective
von
Neumann Algebras
.353
IV.2.3 Normal Cross Norms
.360
IV.2.4
Semidiscrete
Factors
.362
IV.2.
5
Amenable
von
Neumann Algebras
.365
IV.2.6 Approximate Finite Dimensionality
.367
IV.2.
7
Invariants and the Classification of Injective
Factors
.367
IV.3 Nuclear and Exact C*-Algebras
.368
IV.3.1 Nuclear C*-Algebras
.368
IV.3.2 Completely Positive Liftings
.374
IV.3.3 Amenability for C*-Algebras
.378
IV.
3.4
Exactness and Subnuclearity
.383
IV.3.5 Group C^Algebras and Crossed Products
.391
V K-Theory and Finiteness
.395
V.I K-Theory for C^Algebras
.395
V.I.I KO-Theory
.396
V.l.2
Κχ
-Theoľy
and Exact Sequences
.402
V.1.3 Further Topics
.408
V.1.4 Bivariant Theories
.411
V.l.5
Axiomatic it-Theory and the Universal
Coefficient. Theorem
.413
V.2 Finiteness
.418
V.2.1 Finite and Properly Infinite
Unital C*-
Algebras
. 418
V.2.2 Nonunital C*-Algebras
.423
V.2.3 Finiteness in Simple C*-Algebras
.430
V.2.4 Ordered Ji-Theory
.434
V.3 Stable Rank and Real Rank
.444
V.3.1 Stable Rank
.445
V.3.2 Real Rank
.452
V.4 Quasidiagonality
.457
V.4.1
Quasidiagonal
Sets of Operators
.457
V.4.2
Quasidiagonal
С*-
Algebras
.460
XX
Contents
V.4.3
Generalized Inductive
Limits .464
References
.479
Index.505 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Blackadar, Bruce 1948- |
| author_GND | (DE-588)111248485 |
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| dewey-full | 512.556 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.556 |
| dewey-search | 512.556 |
| dewey-sort | 3512.556 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Book |
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| id | DE-604.BV021268155 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T13:43:44Z |
| indexdate | 2024-07-09T20:34:17Z |
| institution | BVB |
| isbn | 3540284869 9783540284864 9783642066733 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014589313 |
| oclc_num | 181481200 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-29T DE-634 DE-11 DE-188 DE-20 DE-83 |
| owner_facet | DE-19 DE-BY-UBM DE-824 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-29T DE-634 DE-11 DE-188 DE-20 DE-83 |
| physical | xx, 517 Seiten |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Springer |
| record_format | marc |
| series | Encyclopaedia of mathematical sciences |
| series2 | Encyclopaedia of mathematical sciences / Operator algebras and non-commutative geometry Encyclopaedia of mathematical sciences |
| spelling | Blackadar, Bruce 1948- Verfasser (DE-588)111248485 aut Operator algebras theory of C*-algebras and von Neumann algebras B. Blackadar Berlin ; Heidelberg Springer [2006] © 2006 xx, 517 Seiten txt rdacontent n rdamedia nc rdacarrier Encyclopaedia of mathematical sciences / Operator algebras and non-commutative geometry 3 Encyclopaedia of mathematical sciences volume 122 C*-algebras Von Neumann algebras C-Stern-Algebra (DE-588)4136693-1 gnd rswk-swf VonNeumann-Algebra (DE-588)4388395-3 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf C-Stern-Algebra (DE-588)4136693-1 s Operatortheorie (DE-588)4075665-8 s DE-604 VonNeumann-Algebra (DE-588)4388395-3 s Erscheint auch als Online-Ausgabe 978-3-540-28517-5 Operator algebras and non-commutative geometry Encyclopaedia of mathematical sciences 3 (DE-604)BV014111511 3 Encyclopaedia of mathematical sciences volume 122 (DE-604)BV024126459 122 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014589313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Blackadar, Bruce 1948- Operator algebras theory of C*-algebras and von Neumann algebras Encyclopaedia of mathematical sciences C*-algebras Von Neumann algebras C-Stern-Algebra (DE-588)4136693-1 gnd VonNeumann-Algebra (DE-588)4388395-3 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4136693-1 (DE-588)4388395-3 (DE-588)4075665-8 |
| title | Operator algebras theory of C*-algebras and von Neumann algebras |
| title_auth | Operator algebras theory of C*-algebras and von Neumann algebras |
| title_exact_search | Operator algebras theory of C*-algebras and von Neumann algebras |
| title_exact_search_txtP | Operator algebras theory of C*-algebras and von Neumann algebras |
| title_full | Operator algebras theory of C*-algebras and von Neumann algebras B. Blackadar |
| title_fullStr | Operator algebras theory of C*-algebras and von Neumann algebras B. Blackadar |
| title_full_unstemmed | Operator algebras theory of C*-algebras and von Neumann algebras B. Blackadar |
| title_short | Operator algebras |
| title_sort | operator algebras theory of c algebras and von neumann algebras |
| title_sub | theory of C*-algebras and von Neumann algebras |
| topic | C*-algebras Von Neumann algebras C-Stern-Algebra (DE-588)4136693-1 gnd VonNeumann-Algebra (DE-588)4388395-3 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | C*-algebras Von Neumann algebras C-Stern-Algebra VonNeumann-Algebra Operatortheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014589313&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014111511 (DE-604)BV024126459 |
| work_keys_str_mv | AT blackadarbruce operatoralgebrastheoryofcalgebrasandvonneumannalgebras |