Fredholm and local spectral theory, with applications to multipliers:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2004
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 444 S. |
| ISBN: | 1402018304 |
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MARC
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| 245 | 1 | 0 | |a Fredholm and local spectral theory, with applications to multipliers |c by Pietro Aiena |
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Record in the Search Index
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| adam_text | FREDHOLM AND LOCAL SPECTRAL THEORY, WITH APPLICATIONS TO MULTIPLIERS BY
PIETRO AIENA DIPARTIMENTO DI MATEMATICA ED APPLICAZIONI, UNIVERSITA DI
PALERMO, PALERMO, ITALY KLUWER ACADEMIC PUBLISHERS DORDRECHT / BOSTON /
LONDON CONTENTS PREFACE 1X CHAPTER 1. THE KATO DECOMPOSITION PROPERTY 1
1. HYPER-KERNEL AND HYPER-RANGE OF AN OPERATOR 2 2. SEMI-REGULAR
OPERATORS ON BANACH SPACES 7 3. ANALYTICAL CORE OF AN OPERATOR 11 4. THE
SEMI-REGULAR SPECTRUM OF AN OPERATOR 14 5. THE GENERALIZED KATO
DECOMPOSITION 24 6. SEMI-PREDHOLM OPERATORS 33 7. QUASI-NILPOTENT PART
OF AN OPERATOR 43 8. TWO SPECTRAL MAPPING THEOREMS 48 CHAPTER 2. THE
SINGLE-VALUED EXTENSION PROPERTY 55 1. LOCAL SPECTRUM AND SVEP 56 2. THE
SVEP AT A POINT 69 3. A LOCAL SPECTRAL MAPPING THEOREM 76 4. ALGEBRAIC
SPECTRAL SUBSPACES 90 5. WEIGHTED SHIFT OPERATORS AND SVEP 99 CHAPTER 3.
THE SVEP AND FREDHOLM THEORY 109 1. ASCENT, DESCENT, AND THE SVEP 110 2.
THE SVEP FOR OPERATORS OF KATO TYPE 119 3. THE SVEP ON THE COMPONENTS OF
P K (T) 127 4. THE FREDHOLM, WEYL, AND BROWDER SPECTRA 132 5.
COMPRESSIONS 143 6. SOME SPECTRAL MAPPING THEOREMS 146 7. ISOLATED
POINTS OF THE SPECTRUM 157 8. WEYL S THEOREM 164 9. RIESZ OPERATORS 179
10. THE SPECTRA OF SOME OPERATORS 182 CHAPTER 4. MULTIPLIERS OF
COMMUTATIVE BANACH ALGEBRAS 191 1. DEFINITIONS AND ELEMENTARY PROPERTIES
192 2. THE HELGASON-WANG FUNCTION 200 3. FIRST SPECTRAL PROPERTIES OF
MULTIPLIERS 210 4. MULTIPLIERS OF GROUP ALGEBRAS 218 5. MULTIPLIERS OF
BANACH ALGEBRAS WITH ORTHOGONAL BASIS 225 VN VLLL CONTENTS 6.
MULTIPLIERS OF COMMUTATIVE H * ALGEBRAS 233 CHAPTER 5. ABSTRACT FREDHOLM
THEORY 239 1. INESSENTIAL IDEALS 240 2. THE SOCLE 244 3. THE SOCLE OF
SEMI-PRIME BANACH ALGEBRAS 249 4. RIESZ ALGEBRAS 255 5. FREDHOLM
ELEMENTS OF BANACH ALGEBRAS 264 6. COMPACT MULTIPLIERS 271 7. WEYL
MULTIPLIERS 279 8. MULTIPLIERS OF TAUBERIAN REGULAR COMMUTATIVE ALGEBRAS
286 9. SOME CONCRETE CASES 292 10. BROWDER SPECTRUM OF A MULTIPLIER 298
CHAPTER 6. DECOMPOSABILITY 309 1. SPECTRAL MAXIMAL SUBSPACES 310 2.
DECOMPOSABLE OPERATORS ON BANACH SPACES 314 3. SUPER-DECOMPOSABLE
OPERATORS . 323 4. DECOMPOSABLE RIGHT SHIFT OPERATORS 331 5.
DECOMPOSABLE MULTIPLIERS 338 6. RIESZ MULTIPLIERS 357 7. DECOMPOSABLE
CONVOLUTION OPERATORS 361 CHAPTER 7. PERTURBATION CLASSES OF OPERATORS
367 1. INESSENTIAL OPERATORS BETWEEN BANACH SPACES 368 2. Q+ AND O_
OPERATORS 382 3. STRICTLY SINGULAR AND STRICTLY COSINGULAR OPERATORS 388
4. IMPROJECTIVE OPERATORS 401 5. INCOMPARABILITY BETWEEN BANACH SPACES
415 BIBLIOGRAPHY 423 INDEX 437
Pietro Aiena
The main aim of this book is to show how the interplay between
Fredholm
theory
and local spectral theory is significant and beautiful. The author begins with the
Kato
decomposition for bounded operators on Banach spaces and develops,
quite systematically, the properties of some important subspaces which play a
significant role in
Fredholm
theory and local spectral theory. A relevant part of
the book concerns the single-valued extension property, through which many of
the classical results of
Fredholm
theory are revisited. Another part of the book is
devoted to the
Fredholm
theory of multipliers of commutative semi-simple
Banach algebras and it is shown that in the framework of multiplier theory the
Gelfand theory,
Fredholm
theory, local spectral theory, and harmonic analysis
are closely interwinded. The concluding part of the book regards some recent
progress in the study of perturbation theory for some classes of operators which
occur in
Fredholm
theory.
This book is intended to be used in graduate courses in operator theory, so the
prerequisites are a background n functional and complex analysis. It will be a
useful companion for professional mathematicians working in the subject, or
interested in applying it to other areas of analysis.
|
| any_adam_object | 1 |
| author | Aiena, Pietro |
| author_facet | Aiena, Pietro |
| author_role | aut |
| author_sort | Aiena, Pietro |
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| dewey-full | 515/.45 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV019439426 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T20:00:11Z |
| institution | BVB |
| isbn | 1402018304 |
| language | English |
| lccn | 2003070283 |
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| physical | XIV, 444 S. |
| publishDate | 2004 |
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| publisher | Kluwer Acad. Publ. |
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| spelling | Aiena, Pietro Verfasser aut Fredholm and local spectral theory, with applications to multipliers by Pietro Aiena Dordrecht [u.a.] Kluwer Acad. Publ. 2004 XIV, 444 S. txt rdacontent n rdamedia nc rdacarrier Banach, Algèbres de Fredholm, Équations de Spectre (Mathématiques) aFredholm equations aSpectral theory (Mathematics) aBanach algebras Lokale Spektraltheorie (DE-588)4168110-1 gnd rswk-swf Fredholm-Theorie (DE-588)4155263-5 gnd rswk-swf Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Lokale Spektraltheorie (DE-588)4168110-1 s Fredholm-Theorie (DE-588)4155263-5 s Banach-Algebra (DE-588)4193187-7 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892959&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892959&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Aiena, Pietro Fredholm and local spectral theory, with applications to multipliers Banach, Algèbres de Fredholm, Équations de Spectre (Mathématiques) aFredholm equations aSpectral theory (Mathematics) aBanach algebras Lokale Spektraltheorie (DE-588)4168110-1 gnd Fredholm-Theorie (DE-588)4155263-5 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| subject_GND | (DE-588)4168110-1 (DE-588)4155263-5 (DE-588)4193187-7 |
| title | Fredholm and local spectral theory, with applications to multipliers |
| title_auth | Fredholm and local spectral theory, with applications to multipliers |
| title_exact_search | Fredholm and local spectral theory, with applications to multipliers |
| title_full | Fredholm and local spectral theory, with applications to multipliers by Pietro Aiena |
| title_fullStr | Fredholm and local spectral theory, with applications to multipliers by Pietro Aiena |
| title_full_unstemmed | Fredholm and local spectral theory, with applications to multipliers by Pietro Aiena |
| title_short | Fredholm and local spectral theory, with applications to multipliers |
| title_sort | fredholm and local spectral theory with applications to multipliers |
| topic | Banach, Algèbres de Fredholm, Équations de Spectre (Mathématiques) aFredholm equations aSpectral theory (Mathematics) aBanach algebras Lokale Spektraltheorie (DE-588)4168110-1 gnd Fredholm-Theorie (DE-588)4155263-5 gnd Banach-Algebra (DE-588)4193187-7 gnd |
| topic_facet | Banach, Algèbres de Fredholm, Équations de Spectre (Mathématiques) aFredholm equations aSpectral theory (Mathematics) aBanach algebras Lokale Spektraltheorie Fredholm-Theorie Banach-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892959&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012892959&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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