Spectral theory of linear operators and spectral systems in Banach algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel [u.a.]
Birkhäuser
2007
|
| Edition: | 2. ed. |
| Series: | Operator theory
139 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Physical Description: | VIII, 439 S. |
| ISBN: | 3764382643 9783764382643 |
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| 100 | 1 | |a Müller, Vladimír |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spectral theory of linear operators and spectral systems in Banach algebras |c Vladimir Müller |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Basel [u.a.] |b Birkhäuser |c 2007 | |
| 300 | |a VIII, 439 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Operator theory |v 139 | |
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Record in the Search Index
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|---|---|
| adam_text |
Contents
Preface
.
vii
Preface
to the Second Edition
. ix
I Banach Algebras
1
Basic Concepts
. 1
2
Commutative Banach algebras
. 18
3
Approximate point spectrum in commutative Banach algebras
. 26
4
Permanently singular elements and removability of spectrum
. 34
5
Non-removable ideals
. 42
6
Axiomatic theory of spectrum
. 51
7
Spectral systems
. 58
8
Basic spectral systems in Banach algebras
. 68
Comments on Chapter I
. 72
II Operators
9
Spectrum of operators
. 85
10
Operators with closed range
. 97
11
Factorization of vector-valued functions
. 106
12
Kato
operators
. 117
13
General inverses and Saphar operators
. 130
14
Local spectrum
. 135
Comments on Chapter II
. 143
III Essential Spectrum
15
Compact operators
. 149
16
Fredholm
and semi-Fredholm operators
. 155
17
Construction of Sadovskii/Buoni,
Harte, Wickstead. 164
18
Perturbation properties of
Fredholm
and semi-Fredholm operators
. 169
19
Essential spectra
. 172
20
Ascent, descent and Browder operators
. 178
vi
Contents
21
Essentially
Kato
operators
. 187
22
Classes of operators defined by means of kernels and ranges
. 197
23
Semiregularities and miscellaneous spectra
. 211
24
Measures of non-compactness and other operator quantities
. 220
Comments on Chapter III
. 228
IV Taylor Spectrum
25
Basic properties
. 237
26
Split spectrum
. 245
27
Some non-linear results
. 252
28
Taylor functional calculus for the split spectrum
. 260
29
Local spectrum for
η
-tuples of operators
. 266
30
Taylor functional calculus
. 271
31
Taylor functional calculus in Banach algebras
. 283
32
fc-regular functions
. 285
33
Stability of index of complexes
. 293
34
Essential Taylor spectrum
. 299
Comments on Chapter IV
. 305
V Orbits and Capacity
35
Joint spectral radius
. 311
36
Capacity
. 321
37
Invariant subset problem and large orbits
. 327
38
Hypercyclic vectors
. 341
39
Weak orbits
. 348
40
Scott Brown technique
. 359
41
Kaplansky's type theorems
. 375
42
Polynomial orbits and local capacity
. 378
Comments on Chapter V
. 387
Appendix
. 393
A.
1
Banach spaces
. 393
A.
2
Analytic vector-valued functions
. 398
A.3 C°°-functions
. 401
A.
4
Semicontinuous set-valued functions
. 403
A.
5
Some geometric properties of Banach spaces
. 404
A.
6
Basic properties of H°°
. 405
Bibliography
. 407
Index
. 429
List of Symbols
. 437 |
| adam_txt |
Contents
Preface
.
vii
Preface
to the Second Edition
. ix
I Banach Algebras
1
Basic Concepts
. 1
2
Commutative Banach algebras
. 18
3
Approximate point spectrum in commutative Banach algebras
. 26
4
Permanently singular elements and removability of spectrum
. 34
5
Non-removable ideals
. 42
6
Axiomatic theory of spectrum
. 51
7
Spectral systems
. 58
8
Basic spectral systems in Banach algebras
. 68
Comments on Chapter I
. 72
II Operators
9
Spectrum of operators
. 85
10
Operators with closed range
. 97
11
Factorization of vector-valued functions
. 106
12
Kato
operators
. 117
13
General inverses and Saphar operators
. 130
14
Local spectrum
. 135
Comments on Chapter II
. 143
III Essential Spectrum
15
Compact operators
. 149
16
Fredholm
and semi-Fredholm operators
. 155
17
Construction of Sadovskii/Buoni,
Harte, Wickstead. 164
18
Perturbation properties of
Fredholm
and semi-Fredholm operators
. 169
19
Essential spectra
. 172
20
Ascent, descent and Browder operators
. 178
vi
Contents
21
Essentially
Kato
operators
. 187
22
Classes of operators defined by means of kernels and ranges
. 197
23
Semiregularities and miscellaneous spectra
. 211
24
Measures of non-compactness and other operator quantities
. 220
Comments on Chapter III
. 228
IV Taylor Spectrum
25
Basic properties
. 237
26
Split spectrum
. 245
27
Some non-linear results
. 252
28
Taylor functional calculus for the split spectrum
. 260
29
Local spectrum for
η
-tuples of operators
. 266
30
Taylor functional calculus
. 271
31
Taylor functional calculus in Banach algebras
. 283
32
fc-regular functions
. 285
33
Stability of index of complexes
. 293
34
Essential Taylor spectrum
. 299
Comments on Chapter IV
. 305
V Orbits and Capacity
35
Joint spectral radius
. 311
36
Capacity
. 321
37
Invariant subset problem and large orbits
. 327
38
Hypercyclic vectors
. 341
39
Weak orbits
. 348
40
Scott Brown technique
. 359
41
Kaplansky's type theorems
. 375
42
Polynomial orbits and local capacity
. 378
Comments on Chapter V
. 387
Appendix
. 393
A.
1
Banach spaces
. 393
A.
2
Analytic vector-valued functions
. 398
A.3 C°°-functions
. 401
A.
4
Semicontinuous set-valued functions
. 403
A.
5
Some geometric properties of Banach spaces
. 404
A.
6
Basic properties of H°°
. 405
Bibliography
. 407
Index
. 429
List of Symbols
. 437 |
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| index_date | 2024-07-02T18:43:59Z |
| indexdate | 2024-07-20T09:24:16Z |
| institution | BVB |
| isbn | 3764382643 9783764382643 |
| language | English |
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| physical | VIII, 439 S. |
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| series | Operator theory |
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| spelling | Müller, Vladimír Verfasser aut Spectral theory of linear operators and spectral systems in Banach algebras Vladimir Müller 2. ed. Basel [u.a.] Birkhäuser 2007 VIII, 439 S. txt rdacontent n rdamedia nc rdacarrier Operator theory 139 Banach algebras Operator theory Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Linearer Operator (DE-588)4167721-3 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Spektraltheorie (DE-588)4116561-5 s Linearer Operator (DE-588)4167721-3 s Banach-Algebra (DE-588)4193187-7 s DE-604 Erscheint auch als Online-Ausgabe 978-3-7643-8265-0 Operator theory 139 (DE-604)BV000000970 139 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2875481&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016067342&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Müller, Vladimír Spectral theory of linear operators and spectral systems in Banach algebras Operator theory Banach algebras Operator theory Spektraltheorie (DE-588)4116561-5 gnd Linearer Operator (DE-588)4167721-3 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4167721-3 (DE-588)4193187-7 |
| title | Spectral theory of linear operators and spectral systems in Banach algebras |
| title_auth | Spectral theory of linear operators and spectral systems in Banach algebras |
| title_exact_search | Spectral theory of linear operators and spectral systems in Banach algebras |
| title_exact_search_txtP | Spectral theory of linear operators and spectral systems in Banach algebras |
| title_full | Spectral theory of linear operators and spectral systems in Banach algebras Vladimir Müller |
| title_fullStr | Spectral theory of linear operators and spectral systems in Banach algebras Vladimir Müller |
| title_full_unstemmed | Spectral theory of linear operators and spectral systems in Banach algebras Vladimir Müller |
| title_short | Spectral theory of linear operators and spectral systems in Banach algebras |
| title_sort | spectral theory of linear operators and spectral systems in banach algebras |
| topic | Banach algebras Operator theory Spektraltheorie (DE-588)4116561-5 gnd Linearer Operator (DE-588)4167721-3 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| topic_facet | Banach algebras Operator theory Spektraltheorie Linearer Operator Banach-Algebra |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=2875481&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016067342&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000970 |
| work_keys_str_mv | AT mullervladimir spectraltheoryoflinearoperatorsandspectralsystemsinbanachalgebras |