Introduction to operator theory and invariant subspaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Amsterdam u.a.
North-Holland
1988
|
| Series: | North-Holland mathematical library
42 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 358 S. |
| ISBN: | 044470521X |
Staff View
MARC
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| 100 | 1 | |a Beauzamy, Bernard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to operator theory and invariant subspaces |c Bernard Beauzamy |
| 264 | 1 | |a Amsterdam u.a. |b North-Holland |c 1988 | |
| 300 | |a XIV, 358 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a North-Holland mathematical library |v 42 | |
| 650 | 7 | |a Opérateurs, Théorie des |2 ram | |
| 650 | 7 | |a Sous-espaces invariants |2 ram | |
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| 650 | 7 | |a calcul fonctionnel |2 inriac | |
| 650 | 7 | |a compacité |2 inriac | |
| 650 | 7 | |a fonction analytique |2 inriac | |
| 650 | 7 | |a opérateur linéaire |2 inriac | |
| 650 | 7 | |a sous-espace invariant |2 inriac | |
| 650 | 7 | |a théorie opérateur |2 inriac | |
| 650 | 7 | |a théorie spectrale |2 inriac | |
| 650 | 4 | |a Invariant subspaces | |
| 650 | 4 | |a Operator theory | |
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| 650 | 0 | 7 | |a Operatortheorie |0 (DE-588)4075665-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
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| adam_text | Table of Contents
Introduction v
Oceano Tex 1
PART I : GENERAL THEORY.
Chapter I : Operators on Finite Dimensional Spaces. 5
1. Spectrum of the operator. 5
2. Minimal Polynomial. 6
3. The analytic functional calculus. 10
4. Computing the operator norm on a Hilbert space. 14
Exercises on Chapter I. 15
Notes and Comments. 17
Complements on Chapter I 17
Chapter II : Elementary Spectral Theory. 19
1. The spectrum of an operator. 21
2. The analytic functional calculus. 27
3. The Invariant Subspace Problem. 32
Exercises on Chapter II. 35
Notes and Comments. 38
Complements on Chapter II. 39
Chapter III : The Orbits of a Linear Operator. 41
0. Introduction. 41
1. Basic Facts. 43
A. The image of a ball by a linear operator. 43
B. Baire Property for operators. 44
C. Rolewicz example of an operator with one hypercyclic point 45
D. The regularity of the sequence (||Tn||)n 0. 47
2. Operators having an orbit which tends to infinity. 48
A. Exponential growths and related topics. 48
B. Quasi exponential growths. 53
xii Table of Contents
C. Polynomial Growths. 57
3. How often can an orbit come back close to 0 ? 62
4. Operators with irregular orbits. 66
5. Hypercyclicity. 71
Exercises on Chapter III. 74
Notes and Comments 75
Part II : COMPACTNESS AND ITS APPLICATIONS.
Chapter IV : Spectral Theory for compact operators. 79
1. Compact operators. 79
2. Spectral Theory for compact operators. 81
3. Spectral Theory for Normal Compact operators on Hilbert spaces. 84
4. Spectral decomposition for compact operators on Hilbert spaces. 88
5. Invariant Subspace for compact operators. 89
6. Commutation between compact operators and C operators. 91
Exercises on Chapter IV. 93
Notes and Comments. 94
Complements on Chapter IV 95
Chapter V : Topologies on the space of operators. 97
1. Nuclear operators. 97
2. The space £(H) as a dual space. 101
Exercises on Chapter V. 115
Notes and Comments. 117
Complements on Chapter V. 117
Part III : BANACH ALGEBRAS TECHNIQUES.
Chapter VI : Banach Algebras. 123
1. Spectral Theory. 123
2. Ideals and Homomorphisms. 126
3. Commutative Banach Algebras. 128
4. Functional Calculus. 131
5. C* algebras. 131
6. An Invariant Subspace Theorem. 134
Exercises on Chapter VI. 137
Notes and Comments. 140
Table of Contents xiii
Chapter VII : Normal Operators. 141
1. Algebra generated by a normal operator. 141
2. Spectral Measures. 143
3. Integration with respect to a spectral measure. 144
4. Spectral Representation of a Normal Operator. 145
5. The spectrum of a multiplication operator. 153
6. Hyperinvariant Subspaces for Normal Operators. 154
Exercises on Chapter VII. 156
Notes and Comments. 157
Complements on Chapter VII. 157
Part IV : ANALYTIC FUNCTIONS.
Chapter VIII : Banach Spaces of Analytic Functions. 163
1. Harmonic and subharmonic functions. 163
2. Basic facts about Fourier Series. 166
3. Hp Spaces. 169
4. Jensen s Formula, Jensen s Inequality. 173
5. Factorization of Hp functions : Inner and Outer functions. 177
6. Factorization of Inner Functions : Blaschke products and ... 179
7. The Disk Algebra A{D). 182
Exercises on Chapter VIII. 187
Notes and Comments. 188
Complements on Chapter VIII. 189
Chapter IX : The Multiplication by ei$ on H2(TVj and L2{Tl). 191
1. The multiplication by tie in H2. 192
2. Szego s Theorem. 195
3. Multiplication by eie on L2{n,d6/2x). 196
4. Multiplication by i on L2[0,1]. 201
Exercises on Chapter IX. 204
Notes and Comments. 206
Complements on Chapter IX. 206
PART V : DILATIONS and EXTENSIONS.
Chapter X : Minimal Dilation of a Contraction. 213
1. Construction of the isometric and unitary dilations. 213
I
xiv Table of Contents
2. Decompositions of the space U . 220
Exercises on Chapter X. 227
Notes and Comments. 228
Complements on Chapter X. 230
Chapter XI : The H°° Functional Calculus. 233
1. Construction of the Calculus. 233
2. The Spectral Theorem for the H°° functional calculus. 239
3. The H°° functional calculus on the algebra generated ... 242
Exercises on Chapter XI. 247
Notes and Comments. 248
Complements on Chapter XI. 248
Chapter XII : Ci Contractions. 249
1. The extension of a C contraction. 250
2. Representing Functions. 251
3. Functional Representation of Convergent Series. 257
4. Connections with Nagy Foias, Dilation Theory. 260
5. The Algebra if (II). 261
6. Two examples. 265
7. The spectrum of T and the spectrum of f. 273
8. Invariant subspaces for the Ci contractions. 277
Exercises on Chapter XII. 282
Notes and Comments. 286
Complements on Chapter XII. 286
Part VI : INVARIANT SUBSPACES.
Chapter XIII : Positive results. 291
1. When is the H°° functional calculus isometric ? 291
2. Invariant Subspaces. 305
Exercises on Chapter XIII. 315
Notes and Comments. 315
Chapter XIV : A Counter Example to the Invariant Subspace Problem. 317
Exercises on Chapter XIV. 340
Notes and Comments 344
Index 347
References 351
|
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| indexdate | 2024-07-09T15:21:02Z |
| institution | BVB |
| isbn | 044470521X |
| language | English |
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| spelling | Beauzamy, Bernard Verfasser aut Introduction to operator theory and invariant subspaces Bernard Beauzamy Amsterdam u.a. North-Holland 1988 XIV, 358 S. txt rdacontent n rdamedia nc rdacarrier North-Holland mathematical library 42 Opérateurs, Théorie des ram Sous-espaces invariants ram algèbre Banach inriac calcul fonctionnel inriac compacité inriac fonction analytique inriac opérateur linéaire inriac sous-espace invariant inriac théorie opérateur inriac théorie spectrale inriac Invariant subspaces Operator theory Invarianter Unterraum (DE-588)4162212-1 gnd rswk-swf Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s DE-604 Invarianter Unterraum (DE-588)4162212-1 s North-Holland mathematical library 42 (DE-604)BV000005206 42 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000555589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Beauzamy, Bernard Introduction to operator theory and invariant subspaces North-Holland mathematical library Opérateurs, Théorie des ram Sous-espaces invariants ram algèbre Banach inriac calcul fonctionnel inriac compacité inriac fonction analytique inriac opérateur linéaire inriac sous-espace invariant inriac théorie opérateur inriac théorie spectrale inriac Invariant subspaces Operator theory Invarianter Unterraum (DE-588)4162212-1 gnd Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4162212-1 (DE-588)4075665-8 |
| title | Introduction to operator theory and invariant subspaces |
| title_auth | Introduction to operator theory and invariant subspaces |
| title_exact_search | Introduction to operator theory and invariant subspaces |
| title_full | Introduction to operator theory and invariant subspaces Bernard Beauzamy |
| title_fullStr | Introduction to operator theory and invariant subspaces Bernard Beauzamy |
| title_full_unstemmed | Introduction to operator theory and invariant subspaces Bernard Beauzamy |
| title_short | Introduction to operator theory and invariant subspaces |
| title_sort | introduction to operator theory and invariant subspaces |
| topic | Opérateurs, Théorie des ram Sous-espaces invariants ram algèbre Banach inriac calcul fonctionnel inriac compacité inriac fonction analytique inriac opérateur linéaire inriac sous-espace invariant inriac théorie opérateur inriac théorie spectrale inriac Invariant subspaces Operator theory Invarianter Unterraum (DE-588)4162212-1 gnd Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Opérateurs, Théorie des Sous-espaces invariants algèbre Banach calcul fonctionnel compacité fonction analytique opérateur linéaire sous-espace invariant théorie opérateur théorie spectrale Invariant subspaces Operator theory Invarianter Unterraum Operatortheorie |
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