The theory of subnormal operators:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[1991]
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| Series: | Mathematical surveys and monographs
Volume 36 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xv, 436 Seiten Diagramme |
| ISBN: | 0821815369 9780821815366 |
Staff View
MARC
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| 245 | 1 | 0 | |a The theory of subnormal operators |c John B. Conway |
| 264 | 1 | |a Providence, Rhode Island |b American Mathematical Society |c [1991] | |
| 264 | 4 | |c © 1991 | |
| 300 | |a xv, 436 Seiten |b Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Mathematical surveys and monographs |v Volume 36 | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xiii
Chapter I. Preliminaries 1
§1 Trace class and Hilbert Schmidt operators 1
§2 Some topologies on 3B{ ) 10
§3 Isometries 13
§4 The unilateral shift of multiplicity 1 18
§5 Direct sums 24
§6 Shifts of higher multiplicity 26
Chapter II. Subnormal Operators: The Elementary Theory 27
§1 Definition and examples 27
§2 Pure operators and the minimal normal extension 37
§3 Quasinormal operators 43
§4 Hyponormal operators 46
§5 Cyclic subnormal operators 50
§6 Weighted shifts 53
§7 Bounded point evaluations 61
§8 Bergman operators 66
§9 Spectral sets 75
§10 The commutant of a subnormal operator 79
§11 The restriction algebra and the functional calculus 85
§12 The C* algebra generated by a subnormal operator 88
§13 Unitary equivalence, similarity, and quasisimilarity 93
Chapter III. Function Theory On The Unit Circle 99
§lCesarosums 99
§2 Convolution on the circle 103
§3 Harmonic functions on the disk 105
§4 Fatou s Theorem 108
§5 Subharmonic functions 114
§6 Hardy spaces 117
§7 The Nevanlinna class 120
§8 Factorization of functions in Nevanlinna class 125
ix
x CONTENTS
§9 The disk algebra 132
§10 The invariant subspace lattice of the unilateral shift 135
§11 Weak star closed ideals in H°° 140
§ 12 Szego s Theorem 141
§ 13 Analytic Toeplitz operators 145
Chapter IV. Hyponormal Operators 149
§1 The real part of a hyponormal operator 150
§2 The Berger Shaw Theorem 152
§3 The area of the spectrum of a hyponormal operator 156
§4 The self commutator of the Bergman operator 156
§5 The decomposition of essentially normal operators 158
Chapter V. Uniform Rational Approximation 163
§1 Function algebras: examples and elementary properties 163
§2 Distributions and some results from analysis 166
§3 The Cauchy transform 173
§4 Invariant subspaces for subnormal operators 181
§5 Vitushkin localization operators 184
§6 T invariant algebras 187
§7 The Shilov boundary 190
§8 Representing measures 193
§9 Harmonic measure 196
§10 Hardy spaces for an arbitrary region 203
§11 Peak points 211
§12 Capacity 216
§ 13 Some applications of analytic capacity 222
§ 14 Dirichlet algebras 226
§ 15 Gleason parts 234
§ 16 The Wermer Embedding Theorem 239
§ 17 Bands of measures 244
§ 18 Annihilating measures 250
§19 Mergelyan s Theorem 253
§20 The double dual of a T invariant algebra 254
§21 The Lautzenheiser Mlak Theorem 260
§22 Davie s Theorem 266
Chapter VI. Weak Star Rational Approximation 277
§1 Weak star closed subalgebras of L°°(n) 277
§2 The envelope 282
§3 Chaumat s Theorem 287
§4 Hx{dK) for a Dirichlet algebra 291
§5 Dirichlet algebras revisited 296
§6 The weak star closure of a Dirichlet algebra 298
§7 The weak star closure of the polynomials 301
CONTENTS xi
Chapter VII. Some Structure Theory For Subnormal Operators 309
§ 1 A decomposition of subnormal operators 309
§2 The minimal normal extension problem for subnormal
operators 315
§3 Spectral mapping theorems 324
§4 Spectral mapping theorems for the essential spectrum 333
§5 A factorization theorem 341
§6 An infinite factorization theorem 352
§7 Full analytic subspaces 357
§8 Reflexivity for subnormal operators 361
§9 Filling in the holes of the spectrum of a normal operator 365
§10 Quasisimilarity revisited 368
Chapter VIII. Bounded Point Evaluations 375
§1 A coloring scheme 375
§2 A sufficient condition for the existence of bounded point
evaluations 384
§3 Heavy barriers exist 389
§4 Bounded point evaluations exist 397
§5 Thomson s Theorem 399
§6 Some applications of Thomson s Theorem 407
Epilogue 409
Bibliography 411
Index 431
List of symbols 435
|
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| id | DE-604.BV004704319 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:16:23Z |
| institution | BVB |
| isbn | 0821815369 9780821815366 |
| language | English |
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| physical | xv, 436 Seiten Diagramme |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Conway, John B. 1939- Verfasser (DE-588)110699882 aut The theory of subnormal operators John B. Conway Providence, Rhode Island American Mathematical Society [1991] © 1991 xv, 436 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 36 Subnormaler Operator (DE-588)4289286-7 gnd rswk-swf Subnormaler Operator (DE-588)4289286-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1263-0 Mathematical surveys and monographs Volume 36 (DE-604)BV000018014 36 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002890105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Conway, John B. 1939- The theory of subnormal operators Mathematical surveys and monographs Subnormaler Operator (DE-588)4289286-7 gnd |
| subject_GND | (DE-588)4289286-7 |
| title | The theory of subnormal operators |
| title_auth | The theory of subnormal operators |
| title_exact_search | The theory of subnormal operators |
| title_full | The theory of subnormal operators John B. Conway |
| title_fullStr | The theory of subnormal operators John B. Conway |
| title_full_unstemmed | The theory of subnormal operators John B. Conway |
| title_short | The theory of subnormal operators |
| title_sort | the theory of subnormal operators |
| topic | Subnormaler Operator (DE-588)4289286-7 gnd |
| topic_facet | Subnormaler Operator |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002890105&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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