Introduction to Banach spaces and algebras:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford [u.a.]
Oxford Univ. Press
2011
|
| Edition: | 1. publ. |
| Series: | Oxford graduate texts in mathematics
20 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 371 S. graph. Darst. |
| ISBN: | 9780199206544 9780199206537 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
Introduction
1
PART
I
INTRODUCTION
TO
BANACH
SPACES
1.
Preliminaries
7
Remarks on set theory
8
Metric spaces and analytic topology
16
Complex analysis
30
2.
Elements of normed spaces
33
Definitions and basic examples
33
Weierstrass
approximation theorems
60
Inner-product spaces
70
Elementary ideas on Fourier series
84
Fourier integrals and Hermite functions
98
3.
Banach spaces
106
Existence of continuous linear functionals
106
Separation theorems
122
Category theorems
128
Dual operators
140
PART II INTRODUCTION TO BANACH ALGEBRAS
4.
Banach algebras
155
Elementary theory
155
Commutative Banach algebras
185
Runge s theorem and the holomorphic functional calculus
211
5.
Representation theory
226
Representations and modules
226
Automatic continuity
241
Variation of the spectral radius
248
6.
Algebras with an involution
260
Banach algebras with an involution
260
C -algebras
269
7.
The
Borei
functional calculus
285
The
Danieli
integral
285
The
Borei
functional calculus and the spectral theorem
294
viii Contents
PART 111 SEVERAL COMPLEX VARIABLES AND BANACH
ALGEBRAS
8.
Introduction to several complex variables
305
Differentiable functions in the plane
305
Functions of several variables
313
Polynomial convexity
326
9.
The holomorphic functional calculus in several variables
339
The main theorem
339
Applications of the functional calculus
345
References
354
Index of terms
363
Index of symbols 36g
|
| adam_txt |
Contents
Introduction
1
PART
I
INTRODUCTION
TO
BANACH
SPACES
1.
Preliminaries
7
Remarks on set theory
8
Metric spaces and analytic topology
16
Complex analysis
30
2.
Elements of normed spaces
33
Definitions and basic examples
33
Weierstrass
approximation theorems
60
Inner-product spaces
70
Elementary ideas on Fourier series
84
Fourier integrals and Hermite functions
98
3.
Banach spaces
106
Existence of continuous linear functionals
106
Separation theorems
122
Category theorems
128
Dual operators
140
PART II INTRODUCTION TO BANACH ALGEBRAS
4.
Banach algebras
155
Elementary theory
155
Commutative Banach algebras
185
Runge's theorem and the holomorphic functional calculus
211
5.
Representation theory
226
Representations and modules
226
Automatic continuity
241
Variation of the spectral radius
248
6.
Algebras with an involution
260
Banach algebras with an involution
260
C'-algebras
269
7.
The
Borei
functional calculus
285
The
Danieli
integral
285
The
Borei
functional calculus and the spectral theorem
294
viii Contents
PART 111 SEVERAL COMPLEX VARIABLES AND BANACH
ALGEBRAS
8.
Introduction to several complex variables
305
Differentiable functions in the plane
305
Functions of several variables
313
Polynomial convexity
326
9.
The holomorphic functional calculus in several variables
339
The main theorem
339
Applications of the functional calculus
345
References
354
Index of terms
363
Index of symbols 36g |
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| index_date | 2024-07-02T21:36:07Z |
| indexdate | 2024-07-09T21:19:38Z |
| institution | BVB |
| isbn | 9780199206544 9780199206537 |
| language | English |
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| physical | VIII, 371 S. graph. Darst. |
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| spelling | Allan, Graham A. Verfasser aut Introduction to Banach spaces and algebras Graham R. Allan. Prepared for publ. by H. Garth Dales 1. publ. Oxford [u.a.] Oxford Univ. Press 2011 VIII, 371 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Oxford graduate texts in mathematics 20 Banach-Algebra (DE-588)4193187-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Banach-Algebra (DE-588)4193187-7 s DE-604 Dales, H. Garth 1944- Verfasser (DE-588)138017204 aut Oxford graduate texts in mathematics 20 (DE-604)BV011416591 20 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016658073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Allan, Graham A. Dales, H. Garth 1944- Introduction to Banach spaces and algebras Oxford graduate texts in mathematics Banach-Algebra (DE-588)4193187-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| subject_GND | (DE-588)4193187-7 (DE-588)4004402-6 |
| title | Introduction to Banach spaces and algebras |
| title_auth | Introduction to Banach spaces and algebras |
| title_exact_search | Introduction to Banach spaces and algebras |
| title_exact_search_txtP | Introduction to Banach spaces and algebras |
| title_full | Introduction to Banach spaces and algebras Graham R. Allan. Prepared for publ. by H. Garth Dales |
| title_fullStr | Introduction to Banach spaces and algebras Graham R. Allan. Prepared for publ. by H. Garth Dales |
| title_full_unstemmed | Introduction to Banach spaces and algebras Graham R. Allan. Prepared for publ. by H. Garth Dales |
| title_short | Introduction to Banach spaces and algebras |
| title_sort | introduction to banach spaces and algebras |
| topic | Banach-Algebra (DE-588)4193187-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | Banach-Algebra Banach-Raum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016658073&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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