Elementary functional analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY
Springer
[2009]
|
| Series: | Graduate texts in mathematics
253 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 207 Seiten Illustrationen, Diagramme 235 mm x 155 mm |
| ISBN: | 9780387855288 9781441927538 |
Staff View
MARC
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| 100 | 1 | |a MacCluer, Barbara D. |e Verfasser |0 (DE-588)137647735 |4 aut | |
| 245 | 1 | 0 | |a Elementary functional analysis |c Barbara D. MacCluer |
| 264 | 1 | |a New York, NY |b Springer |c [2009] | |
| 264 | 4 | |c © 2009 | |
| 300 | |a X, 207 Seiten |b Illustrationen, Diagramme |c 235 mm x 155 mm | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 253 | |
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Record in the Search Index
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|---|---|
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| adam_text |
Contents
Preface
.
vu
1
Hilbert
Space Preliminaries
. 1
1.1 Normed Linear Spaces. 2
1.2
Orthogonality
. 10
1.3 Hilbert Space
Geometry
. 12
1.4 Linear Functionals. 15
1.5
Orthonormal
Bases. 19
1.6
Exercises
. 23
2 Operator
Theory
Basics. 31
2.1
Bounded
Linear Operators. 31
2.2
Adjoints
of
Hilbert Space Operators. 34
2.3
Adjoints
of Banach
Space Operators. 41
2.4
Exercises
. 43
3 The Big
Three
. 49
3.1 The Hahn-Banach Theorem. 50
3.2
Principle of
Uniform Boundedness. 55
3.3
Open Mapping and Closed Graph Theorems
. 61
3.4
Quotient Spaces
. 66
3.5
Banach and the Scottish
Café
. 67
3.6
Exercises
. 68
4
Compact Operators
. 77
4.1
Finite-Dimensional Spaces
. 77
4.2
Compact Operators
. 80
4.3
A Preliminary Spectral Theorem
. 87
4.4
The Invariant Subspace Problem
. 94
4.5
Introduction to the Spectrum
. 96
4.6
The
Fredholm
Alternative
.,. 99
4.7
Exercises
.101
x
Contents
5
Banach and
C-AIgebras.107
5.1 First
Examples.
108
5.2
Results on Spectra
.110
5.3
Ideals and Homomorphisms
.120
5.4
Commutative Banach Algebras
.124
5.5
Weak Topologies
.127
5.6
The Gelfand Transform
.132
5.7
The Continuous Functional Calculus
.140
5.8
Fredholm
Operators
.143
5.9
Exercises
.146
6
The Spectral Theorem
.157
6.1
Normal Operators Are Multiplication Operators
.157
6.2
Spectral Measures
.165
6.3
Exercises
.183
Appendix A: Real Analysis Topics
.187
A.I Measures
.187
A.2 Integration
.190
A.3
W
Spaces
.196
A.4 The Stone-Weierstrass Theorem
.197
A.5 Positive Linear Functional on C(X)
.198
References
.201
Index
.203 |
| any_adam_object | 1 |
| author | MacCluer, Barbara D. |
| author_GND | (DE-588)137647735 |
| author_facet | MacCluer, Barbara D. |
| author_role | aut |
| author_sort | MacCluer, Barbara D. |
| author_variant | b d m bd bdm |
| building | Verbundindex |
| bvnumber | BV035213510 |
| callnumber-first | Q - Science |
| callnumber-label | QA320 |
| callnumber-raw | QA320 |
| callnumber-search | QA320 |
| callnumber-sort | QA 3320 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SI 990 SK 600 SK 620 |
| ctrlnum | (OCoLC)258078575 (DE-599)DNB990588157 |
| dewey-full | 515.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.7 |
| dewey-search | 515.7 |
| dewey-sort | 3515.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV035213510 |
| illustrated | Illustrated |
| indexdate | 2025-02-20T06:36:58Z |
| institution | BVB |
| isbn | 9780387855288 9781441927538 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017019707 |
| oclc_num | 258078575 |
| open_access_boolean | |
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| owner_facet | DE-20 DE-824 DE-355 DE-BY-UBR DE-706 DE-703 DE-83 DE-898 DE-BY-UBR DE-188 DE-862 DE-BY-FWS DE-11 |
| physical | X, 207 Seiten Illustrationen, Diagramme 235 mm x 155 mm |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spellingShingle | MacCluer, Barbara D. Elementary functional analysis Graduate texts in mathematics Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd Online-Ressource (DE-588)4511937-5 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4018916-8 (DE-588)4511937-5 (DE-588)4075665-8 (DE-588)4123623-3 |
| title | Elementary functional analysis |
| title_auth | Elementary functional analysis |
| title_exact_search | Elementary functional analysis |
| title_full | Elementary functional analysis Barbara D. MacCluer |
| title_fullStr | Elementary functional analysis Barbara D. MacCluer |
| title_full_unstemmed | Elementary functional analysis Barbara D. MacCluer |
| title_short | Elementary functional analysis |
| title_sort | elementary functional analysis |
| topic | Functional analysis Funktionalanalysis (DE-588)4018916-8 gnd Online-Ressource (DE-588)4511937-5 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Functional analysis Funktionalanalysis Online-Ressource Operatortheorie Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017019707&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000067 |
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Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 600 M128 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |