Introduction to Banach spaces and algebras:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Oxford
Oxford University Press
2011
|
| Series: | Oxford graduate texts in mathematics
20 |
| Subjects: | |
| Online Access: | FAW01 FAW02 Volltext |
| Item Description: | Description based on print version record |
| Physical Description: | 1 online resource (vii, 371 pages) |
| ISBN: | 0191548545 0199206538 0199206546 9780191548543 9780199206537 9780199206544 |
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| 245 | 1 | 0 | |a Introduction to Banach spaces and algebras |c Graham Allan ; prepared for publication by H. Garth Dales |
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| 300 | |a 1 online resource (vii, 371 pages) | ||
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| 490 | 0 | |a Oxford graduate texts in mathematics |v 20 | |
| 500 | |a Description based on print version record | ||
| 505 | 8 | |a Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources | |
| 505 | 8 | |a pt. I. Introduction to Banach spaces. 1. Preliminaries -- 2. Elements of normed spaces -- 3. Banach spaces -- pt. II. Introduction to Banach algebras. 4. Banach algebras -- 5. Representation theory -- 6. Algebras with an involution -- 7. The Borel functional calculus -- pt. III. Several complex variables and Banach algebras. 8. Introduction to several complex variables -- 9. The holomorphic functional calculus in several variables | |
| 650 | 7 | |a MATHEMATICS / Calculus |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Mathematical Analysis |2 bisacsh | |
| 650 | 7 | |a Banach algebras |2 fast | |
| 650 | 7 | |a Banach spaces |2 fast | |
| 650 | 4 | |a Banach spaces | |
| 650 | 4 | |a Banach algebras | |
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| 700 | 1 | |a Dales, H. G. |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |a Allan, Graham R |t , -2007. Introduction to Banach spaces and algebras |
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Record in the Search Index
| _version_ | 1804175393283899392 |
|---|---|
| any_adam_object | |
| author | Allan, Graham R. -2007 |
| author_facet | Allan, Graham R. -2007 |
| author_role | aut |
| author_sort | Allan, Graham R. -2007 |
| author_variant | g r a gr gra |
| building | Verbundindex |
| bvnumber | BV043034458 |
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| contents | Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources pt. I. Introduction to Banach spaces. 1. Preliminaries -- 2. Elements of normed spaces -- 3. Banach spaces -- pt. II. Introduction to Banach algebras. 4. Banach algebras -- 5. Representation theory -- 6. Algebras with an involution -- 7. The Borel functional calculus -- pt. III. Several complex variables and Banach algebras. 8. Introduction to several complex variables -- 9. The holomorphic functional calculus in several variables |
| ctrlnum | (OCoLC)861693022 (DE-599)BVBBV043034458 |
| dewey-full | 515.732 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.732 |
| dewey-search | 515.732 |
| dewey-sort | 3515.732 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043034458 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:15:34Z |
| institution | BVB |
| isbn | 0191548545 0199206538 0199206546 9780191548543 9780199206537 9780199206544 |
| language | English |
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| physical | 1 online resource (vii, 371 pages) |
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| publishDate | 2011 |
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| spelling | Allan, Graham R. -2007 Verfasser aut Introduction to Banach spaces and algebras Graham Allan ; prepared for publication by H. Garth Dales Oxford Oxford University Press 2011 1 online resource (vii, 371 pages) txt rdacontent c rdamedia cr rdacarrier Oxford graduate texts in mathematics 20 Description based on print version record Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources pt. I. Introduction to Banach spaces. 1. Preliminaries -- 2. Elements of normed spaces -- 3. Banach spaces -- pt. II. Introduction to Banach algebras. 4. Banach algebras -- 5. Representation theory -- 6. Algebras with an involution -- 7. The Borel functional calculus -- pt. III. Several complex variables and Banach algebras. 8. Introduction to several complex variables -- 9. The holomorphic functional calculus in several variables MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Banach algebras fast Banach spaces fast Banach spaces Banach algebras 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 1\p DE-604 Dales, H. G. Sonstige oth Erscheint auch als Druck-Ausgabe Allan, Graham R , -2007. Introduction to Banach spaces and algebras http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=655428 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Allan, Graham R. -2007 Introduction to Banach spaces and algebras Banach spaces and algebras are a key topic of pure mathematics. Graham Allan's careful and detailed introductory account will prove essential reading for anyone wishing to specialise in functional analysis and is aimed at final year undergraduates or masters level students. Based on the author's lectures to fourth year students at Cambridge University, the book assumes knowledge typical of first degrees in mathematics, including metric spaces, analytic topology, and complex analysis. However, readers are not expected to be familiar with the Lebesgue theory of measure and integration. The text begins by giving the basic theory of Banach spaces, including dual spaces and bounded linear operators. It establishes forms of the theorems that are the pillars of functional analysis, including the Banach-Alaoglu, Hahn-Banach, uniform boundedness, open mapping, and closed graph theorems. There are applications to Fourier series and operators on Hilbert spaces. The main body of the text is an introduction to the theory of Banach algebras. A particular feature is the detailed account of the holomorphic functional calculus in one and several variables; all necessary background theory in one and several complex variables is fully explained, with many examples and applications considered. Throughout, exercises at sections ends help readers test their understanding, while extensive notes point to more advanced topics and sources pt. I. Introduction to Banach spaces. 1. Preliminaries -- 2. Elements of normed spaces -- 3. Banach spaces -- pt. II. Introduction to Banach algebras. 4. Banach algebras -- 5. Representation theory -- 6. Algebras with an involution -- 7. The Borel functional calculus -- pt. III. Several complex variables and Banach algebras. 8. Introduction to several complex variables -- 9. The holomorphic functional calculus in several variables MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Banach algebras fast Banach spaces fast Banach spaces Banach algebras 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_full | Introduction to Banach spaces and algebras Graham Allan ; prepared for publication by H. Garth Dales |
| title_fullStr | Introduction to Banach spaces and algebras Graham Allan ; prepared for publication by H. Garth Dales |
| title_full_unstemmed | Introduction to Banach spaces and algebras Graham Allan ; prepared for publication by H. Garth Dales |
| title_short | Introduction to Banach spaces and algebras |
| title_sort | introduction to banach spaces and algebras |
| topic | MATHEMATICS / Calculus bisacsh MATHEMATICS / Mathematical Analysis bisacsh Banach algebras fast Banach spaces fast Banach spaces Banach algebras Banach-Algebra (DE-588)4193187-7 gnd Banach-Raum (DE-588)4004402-6 gnd |
| topic_facet | MATHEMATICS / Calculus MATHEMATICS / Mathematical Analysis Banach algebras Banach spaces Banach-Algebra Banach-Raum |
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