Foundations of free noncommutative function theory:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Schriftenreihe: | Mathematical surveys and monographs
Volume 199 |
| Schlagworte: |
Sequences, series, summability
> Convergence and divergence of infinite limiting processes
> Convergence and divergence of series and sequences
Functional analysis
> Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.)
> Noncommutative function spaces
Functional analysis
> Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.)
> Free probability and free operator algebras
|
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | vi, 183 Seiten |
| ISBN: | 9781470416973 |
Internformat
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| 650 | 4 | |a Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of series and sequences | |
| 650 | 4 | |a Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Noncommutative function spaces | |
| 650 | 4 | |a Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Free probability and free operator algebras | |
| 650 | 4 | |a Operator theory -- General theory of linear operators -- Functional calculus | |
| 650 | 4 | |a Operator theory -- Linear spaces and algebras of operators -- Operator spaces (= matricially normed spaces) | |
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Datensatz im Suchindex
| _version_ | 1804174777769787392 |
|---|---|
| adam_text | Titel: Foundations of free noncommutative function theory
Autor: Kaliuzhnyi-Verbovetskyi, Dmitry S
Jahr: 2014
Contents
Chapter 1. Introduction 1
1.1. Noncommutative (nc) functions: examples and genesis 3
1.2. NC sets, nc functions, and nc difference-differential calculus 5
1.3. Applications of the Taylor-Taylor formula 9
1.4. An overview 11
Acknowledgements 14
Chapter 2. NC functions and their difference-differential calculus 15
2.1. Definition of nc functions 15
2.2. NC difference-differential Operators 17
2.3. Basic rules of nc difference-differential calculus 22
2.4. First order difference formulae 25
2.5. Properties of Auf(X,Y) and Al/(X,Y) as functions of X and Y 27
2.6. Directional nc difference-differential Operators 31
Chapter 3. Higher order nc functions and their difference-differential calculus 33
3.1. Higher order nc functions 33
3.2. Higher order nc difference-differential Operators 41
3.3. First order difference formulae for higher order nc functions 54
3.4. NC integrability 56
3.5. Higher order directional nc difference-differential Operators 57
Chapter 4. The Taylor-Taylor formula 61
Chapter 5. NC functions on nilpotent matrices 67
5.1. From nc functions to nc power series 67
5.2. From nc power series to nc functions 70
Chapter 6. NC polynomials vs. polynomials in matrix entries 77
Chapter 7. NC analyticity and convergence of TT series 83
7.1. Analytic nc functions 83
7.2. Uniformly-open topology over an Operator space 94
7.3. Uniformly analytic nc functions 97
7.4. Analytic and uniformly analytic higher order nc functions 109
Chapter 8. Convergence of nc power series 125
8.1. Finitely open topology 125
8.2. Norm topology 130
8.3. Uniformly-open topology 133
Chapter 9. Direct summands extensions of nc sets and nc functions 155
V
vi CONTENTS
(Some) earlier work on nc functions 167
Appendix A. Similarity invariant envelopes and extension of nc functions 171
Bibliography 175
Index 181
|
| any_adam_object | 1 |
| author | Kaliuzhnyi-Verbovetskyi, Dmitry S. 1965- Vinnikov, Victor 1967- |
| author_GND | (DE-588)1065676271 (DE-588)1065676417 |
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| id | DE-604.BV042607660 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:05:47Z |
| institution | BVB |
| isbn | 9781470416973 |
| language | English |
| lccn | 2014025799 |
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| owner_facet | DE-19 DE-BY-UBM DE-20 DE-11 |
| physical | vi, 183 Seiten |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Kaliuzhnyi-Verbovetskyi, Dmitry S. 1965- Verfasser (DE-588)1065676271 aut Foundations of free noncommutative function theory Dmitry S. Kaliuzhnyi-Verbovetskyi ; Victor Vinnikov Providence, Rhode Island American Mathematical Society [2014] © 2014 vi, 183 Seiten txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 199 Functional analysis Noncommutative algebras Noncommutative function spaces Nonassociative rings and algebras -- General nonassociative rings -- Free algebras Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of series and sequences Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Noncommutative function spaces Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Free probability and free operator algebras Operator theory -- General theory of linear operators -- Functional calculus Operator theory -- Linear spaces and algebras of operators -- Operator spaces (= matricially normed spaces) Funktionalanalysis (DE-588)4018916-8 gnd rswk-swf Funktionalanalysis (DE-588)4018916-8 s DE-604 Vinnikov, Victor 1967- Verfasser (DE-588)1065676417 aut Erscheint auch als Online-Ausgabe 978-1-4704-2001-7 Mathematical surveys and monographs Volume 199 (DE-604)BV000018014 199 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028040594&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaliuzhnyi-Verbovetskyi, Dmitry S. 1965- Vinnikov, Victor 1967- Foundations of free noncommutative function theory Mathematical surveys and monographs Functional analysis Noncommutative algebras Noncommutative function spaces Nonassociative rings and algebras -- General nonassociative rings -- Free algebras Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of series and sequences Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Noncommutative function spaces Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Free probability and free operator algebras Operator theory -- General theory of linear operators -- Functional calculus Operator theory -- Linear spaces and algebras of operators -- Operator spaces (= matricially normed spaces) Funktionalanalysis (DE-588)4018916-8 gnd |
| subject_GND | (DE-588)4018916-8 |
| title | Foundations of free noncommutative function theory |
| title_auth | Foundations of free noncommutative function theory |
| title_exact_search | Foundations of free noncommutative function theory |
| title_full | Foundations of free noncommutative function theory Dmitry S. Kaliuzhnyi-Verbovetskyi ; Victor Vinnikov |
| title_fullStr | Foundations of free noncommutative function theory Dmitry S. Kaliuzhnyi-Verbovetskyi ; Victor Vinnikov |
| title_full_unstemmed | Foundations of free noncommutative function theory Dmitry S. Kaliuzhnyi-Verbovetskyi ; Victor Vinnikov |
| title_short | Foundations of free noncommutative function theory |
| title_sort | foundations of free noncommutative function theory |
| topic | Functional analysis Noncommutative algebras Noncommutative function spaces Nonassociative rings and algebras -- General nonassociative rings -- Free algebras Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of series and sequences Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Noncommutative function spaces Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Free probability and free operator algebras Operator theory -- General theory of linear operators -- Functional calculus Operator theory -- Linear spaces and algebras of operators -- Operator spaces (= matricially normed spaces) Funktionalanalysis (DE-588)4018916-8 gnd |
| topic_facet | Functional analysis Noncommutative algebras Noncommutative function spaces Nonassociative rings and algebras -- General nonassociative rings -- Free algebras Sequences, series, summability -- Convergence and divergence of infinite limiting processes -- Convergence and divergence of series and sequences Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Noncommutative function spaces Functional analysis -- Selfadjoint operator algebras (C *-algebras, von Neumann (W *-) algebras, etc.) -- Free probability and free operator algebras Operator theory -- General theory of linear operators -- Functional calculus Operator theory -- Linear spaces and algebras of operators -- Operator spaces (= matricially normed spaces) Funktionalanalysis |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028040594&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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