Nest algebras: triangular forms for operator algebras on Hilbert space
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Harlow, Essex
Longman Scientific & Techn.
1988
|
| Edition: | 1. publ. |
| Series: | Pitman research notes in mathematics series
191 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 412 S. |
| ISBN: | 0582019931 |
Staff View
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| 100 | 1 | |a Davidson, Kenneth R. |d 1951- |e Verfasser |0 (DE-588)139971599 |4 aut | |
| 245 | 1 | 0 | |a Nest algebras |b triangular forms for operator algebras on Hilbert space |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Harlow, Essex |b Longman Scientific & Techn. |c 1988 | |
| 300 | |a 412 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Pitman research notes in mathematics series |v 191 | |
| 650 | 4 | |a Algèbre Neumann | |
| 650 | 4 | |a Algèbre opérateur | |
| 650 | 4 | |a Algèbre triangulaire | |
| 650 | 4 | |a Algèbres de Von Neumann | |
| 650 | 7 | |a C - Algèbres |2 ram | |
| 650 | 4 | |a C*-algèbre | |
| 650 | 4 | |a C*-algèbres | |
| 650 | 4 | |a Opérateurs compacts | |
| 650 | 7 | |a Von Neumann, Algèbres de |2 ram | |
| 650 | 4 | |a C*-algebras | |
| 650 | 4 | |a Compact operators | |
| 650 | 4 | |a Von Neumann algebras | |
| 650 | 0 | 7 | |a Triangulare Operatoralgebra |0 (DE-588)4398220-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Operatoralgebra |0 (DE-588)4129366-6 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804115735211933696 |
|---|---|
| adam_text | Table of Contents
0. Background
0.1. Banach Algebras; 0.2. C Algebras;
0.3. Von Neumann Algebras;
0.4. Compact Operators; 0.5. Bounded Operators. 1
1. Compact Operators
1. Ideals of Compact Operators
Singular values, Cp classes, trace, duality. 11
2. Triangular Algebras
Nests, nest algebras, reflexivity, order type of a nest, the
diagonal, intervals and homomorphisms. 22
3. Triangular Forms for Compact Operators
Invariant subspaces for compact operators,
Ringrose s Theorem, finite rank operators, Erdos Density Theorem,
Lidskii s Theorem on the trace. 30
4. Triangular Truncation
Unboundedness of truncation, an integral formula,
truncation in C2, the Macaev ideal, truncation
in Cj and Cu and its converse. 39
5. The Volterra Operator
Characterization up to unitary equivalence,
invariant subspaces, singular values, the commutant,
generators for 1{LatV). 51
II Structure of Nest Algebras
6. The Radical
Hom(M,2), test intervals, characterization
of the radical, representations of T[f/)/rad()/),
centre of T{yf)/rad(U). 61
7. Unitary Invariants for Nests
Spectral measure of a nest, connection with
self adjoint operators, maximal abelian von Neumann algebras,
multiplicity, classification of abelian von Neumann algebras,
unitary invariants for self adjoint operators,
unitary invariants for nests, multiplicity
free nests, an open problem. 73
8. Expectations
Basic properties, existence of expectations,
uniqueness ?, invariant means, diagonal truncation
and triangular truncation revisited,
the R°%X) ideal. 87
0. Distance Formulae
Arveson s formula for the distance to a nest algebra,
estimates for the distance to AF von Neumann algebras,
the abelian case, Stampfli s formula for distance
to the scalars. 98
10. Derivations of C* Algebras
Bimodules, automatic continuity of derivations of
C* algebras, the bidual of a C* algebra,
weak* continuity of derivations, derivations of
AF von Neumann algebras are inner,
the Johnson Parrott Theorem. 110
11. M Ideals
A/ ideals, best approximation, ideals of
C algebras, hereditary properties,
approximate identities, distance formulae. 120
12. Quasitriangular Algebras
The algebra QT[M), QT{M), the
distance to QT{M); a characterization of
Q.T{M) QT{M), similarity and
approximate unitary equivalence of nests, an example. 131
13. Similarity and Approximate Unitary Equivalence
Andersen s Theorem approximate unitary equivalence
of all continuous nests; similarity of continuous nests,
absolute continuity and partitions,
Similarity Theorem, the R° }/) ideal. 150
m Additional Topics
14. Factorization
Factorization of positive operators as P = T*T for T in
T[M), factorization of invertible operators in 7(.V),
the role of the Macaev ideal, outer operators, factorization
in well ordered nests. 169
15. Reflexivity, Ideals, and Bimodules
1. Utility grade tensor products; 2. Reflexivity,
bimodules for a masa in B(M), nest algebras;
3. Weak* closed ideals of 7(.W), generators;
4. Interpolation: when Aj,...^,, generate
7(.W) as a left ideal; 5. Invariant operator ranges,
Foias s Theorem, invariant ranges for CSL algebras. 184
IS. Duality
The predual of 7(.W), extreme points, new proofs
of Erdos Density Theorem, Arveson s Distance Formula,
and Lidskii s Theorem, decomposition of trace class
operators in 1[M) as sums of
rank one operators. 208
17. Isomorphisms
Isomorphisms of masas, automatic continuity of
isomorphisms of nest algebras, isomorphisms of the
finite rank operators, automorphisms of nest algebras
are spatial, the outer automorphism group, the
quasitriangular algebra and its outer automorphism group. 224
18. Perturbations of Operator Algebras
Hausdorff distance for subspaces, perturbation of
CSL algebras, nest algebras, perturbation of abelian
von Neumann algebras and their commutants. 246
19. Derivations of Nest Algebras
Automatic continuity, derivations of 7(.V) are
inner, derivations of QT[M) are inner, essential
commutant of 7(.V), compact derivations, pointwise
limits of derivations. Appendix: Ko of a nest
algebra. Notes; cohomology of nest algebras. 258
20. Representation and Dilation Theory
1. Dilation theory for single operators, Ando s Theorem,
Sz. Nagy Foias Lifting Theorem. 2. Completely positive maps,
Arveson s Extension Theorem, Stinespring s Dilation Theorem.
3. Representations of nest algebras, semidiscreteness,
dilation theory. 4. Lifting theorems for nest algebras,
analogues of Ando and Sz. Nagy Foias Theorems,
Parrott s example. 279
21. Operators in Nest Algebras
1. Unicellular operators, construction of examples.
2. Unitary orbits of nest algebras, Herrero s Theorem. 306
IV CSL Algebras
22. Commutative Subspace Lattices
A representation theorem, pseudo integral operators,
reflexivity, AmiD(L), synthetic lattices,
generators. Appendix: product formula for pseudo
integral operators. 327
23. Complete Distributivity and Compact Operators
Completely distributive lattices, rank one operators
in CSL algebras SOT compactness, finite rank operators,
examples of CSL algebras with few compact operators. 351
24. Failure of the Distance Formula
Examples of CSL algebras which are not hyperreflexive,
the dual product construction. 366
25. Open Problems 377
BIBLIOGRAPHY 383
INDEX 408
|
| any_adam_object | 1 |
| author | Davidson, Kenneth R. 1951- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 515 - Analysis |
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| dewey-search | 512/.55 515/.7246 |
| dewey-sort | 3512 255 |
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| discipline | Mathematik |
| edition | 1. publ. |
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| spelling | Davidson, Kenneth R. 1951- Verfasser (DE-588)139971599 aut Nest algebras triangular forms for operator algebras on Hilbert space 1. publ. Harlow, Essex Longman Scientific & Techn. 1988 412 S. txt rdacontent n rdamedia nc rdacarrier Pitman research notes in mathematics series 191 Algèbre Neumann Algèbre opérateur Algèbre triangulaire Algèbres de Von Neumann C - Algèbres ram C*-algèbre C*-algèbres Opérateurs compacts Von Neumann, Algèbres de ram C*-algebras Compact operators Von Neumann algebras Triangulare Operatoralgebra (DE-588)4398220-7 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s DE-604 Triangulare Operatoralgebra (DE-588)4398220-7 s DE-188 Pitman research notes in mathematics series 191 (DE-604)BV000022845 191 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000802537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Davidson, Kenneth R. 1951- Nest algebras triangular forms for operator algebras on Hilbert space Pitman research notes in mathematics series Algèbre Neumann Algèbre opérateur Algèbre triangulaire Algèbres de Von Neumann C - Algèbres ram C*-algèbre C*-algèbres Opérateurs compacts Von Neumann, Algèbres de ram C*-algebras Compact operators Von Neumann algebras Triangulare Operatoralgebra (DE-588)4398220-7 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| subject_GND | (DE-588)4398220-7 (DE-588)4129366-6 |
| title | Nest algebras triangular forms for operator algebras on Hilbert space |
| title_auth | Nest algebras triangular forms for operator algebras on Hilbert space |
| title_exact_search | Nest algebras triangular forms for operator algebras on Hilbert space |
| title_full | Nest algebras triangular forms for operator algebras on Hilbert space |
| title_fullStr | Nest algebras triangular forms for operator algebras on Hilbert space |
| title_full_unstemmed | Nest algebras triangular forms for operator algebras on Hilbert space |
| title_short | Nest algebras |
| title_sort | nest algebras triangular forms for operator algebras on hilbert space |
| title_sub | triangular forms for operator algebras on Hilbert space |
| topic | Algèbre Neumann Algèbre opérateur Algèbre triangulaire Algèbres de Von Neumann C - Algèbres ram C*-algèbre C*-algèbres Opérateurs compacts Von Neumann, Algèbres de ram C*-algebras Compact operators Von Neumann algebras Triangulare Operatoralgebra (DE-588)4398220-7 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| topic_facet | Algèbre Neumann Algèbre opérateur Algèbre triangulaire Algèbres de Von Neumann C - Algèbres C*-algèbre C*-algèbres Opérateurs compacts Von Neumann, Algèbres de C*-algebras Compact operators Von Neumann algebras Triangulare Operatoralgebra Operatoralgebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000802537&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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