The Isometric Theory of Classical Banach Spaces:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1974
|
| Series: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
208 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1 < p < 00, then it is well known that X=L (j1,IR) where 1/p+1/q=1 and if p=oo, then X=L (v,lR) for q j some measure v. Thus, the only case where a space is obtained which is not truly classical is when p = 1. This class of spaces is known as L - 1 predual spaces since their duals are L type. It includes some well known j subclasses such as spaces of the type C(T, IR) for T a compact Hausdorff space and abstract M spaces. The structure theorems concern necessary and sufficient conditions that a general Banach space is linearly isometric to a classical Banach space. They are framed in terms of conditions on the norm of the space X, conditions on the dual space X*, and on (finite dimensional) subspaces of X. Since most of these spaces are Banach lattices and Banach algebras, characterizations among theses classes are also given |
| Physical Description: | 1 Online-Ressource (X, 272 p) |
| ISBN: | 9783642657627 9783642657641 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-65762-7 |
Staff View
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| 500 | |a The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1 < p < 00, then it is well known that X=L (j1,IR) where 1/p+1/q=1 and if p=oo, then X=L (v,lR) for q j some measure v. Thus, the only case where a space is obtained which is not truly classical is when p = 1. This class of spaces is known as L - 1 predual spaces since their duals are L type. It includes some well known j subclasses such as spaces of the type C(T, IR) for T a compact Hausdorff space and abstract M spaces. The structure theorems concern necessary and sufficient conditions that a general Banach space is linearly isometric to a classical Banach space. They are framed in terms of conditions on the norm of the space X, conditions on the dual space X*, and on (finite dimensional) subspaces of X. Since most of these spaces are Banach lattices and Banach algebras, characterizations among theses classes are also given | ||
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642657627 9783642657641 |
| issn | 0072-7830 |
| language | English |
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| spelling | Lacey, H. Elton Verfasser aut The Isometric Theory of Classical Banach Spaces by H. Elton Lacey Berlin, Heidelberg Springer Berlin Heidelberg 1974 1 Online-Ressource (X, 272 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 208 0072-7830 The purpose of this book is to present the main structure theorems in the isometric theory of classical Banach spaces. Elements of general topology, measure theory, and Banach spaces are assumed to be familiar to the reader. A classical Banach space is a Banach space X whose dual space is linearly isometric to Lp(j1, IR) (or Lp(j1, CC) in the complex case) for some measure j1 and some 1 ~ p ~ 00. If 1 < p < 00, then it is well known that X=L (j1,IR) where 1/p+1/q=1 and if p=oo, then X=L (v,lR) for q j some measure v. Thus, the only case where a space is obtained which is not truly classical is when p = 1. This class of spaces is known as L - 1 predual spaces since their duals are L type. It includes some well known j subclasses such as spaces of the type C(T, IR) for T a compact Hausdorff space and abstract M spaces. The structure theorems concern necessary and sufficient conditions that a general Banach space is linearly isometric to a classical Banach space. They are framed in terms of conditions on the norm of the space X, conditions on the dual space X*, and on (finite dimensional) subspaces of X. Since most of these spaces are Banach lattices and Banach algebras, characterizations among theses classes are also given Mathematics Mathematics, general Mathematik Banach-Raum (DE-588)4004402-6 gnd rswk-swf Isometrie Mathematik (DE-588)4456598-7 gnd rswk-swf Banach-Raum (DE-588)4004402-6 s Isometrie Mathematik (DE-588)4456598-7 s 1\p DE-604 https://doi.org/10.1007/978-3-642-65762-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Lacey, H. Elton The Isometric Theory of Classical Banach Spaces Mathematics Mathematics, general Mathematik Banach-Raum (DE-588)4004402-6 gnd Isometrie Mathematik (DE-588)4456598-7 gnd |
| subject_GND | (DE-588)4004402-6 (DE-588)4456598-7 |
| title | The Isometric Theory of Classical Banach Spaces |
| title_auth | The Isometric Theory of Classical Banach Spaces |
| title_exact_search | The Isometric Theory of Classical Banach Spaces |
| title_full | The Isometric Theory of Classical Banach Spaces by H. Elton Lacey |
| title_fullStr | The Isometric Theory of Classical Banach Spaces by H. Elton Lacey |
| title_full_unstemmed | The Isometric Theory of Classical Banach Spaces by H. Elton Lacey |
| title_short | The Isometric Theory of Classical Banach Spaces |
| title_sort | the isometric theory of classical banach spaces |
| topic | Mathematics Mathematics, general Mathematik Banach-Raum (DE-588)4004402-6 gnd Isometrie Mathematik (DE-588)4456598-7 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Banach-Raum Isometrie Mathematik |
| url | https://doi.org/10.1007/978-3-642-65762-7 |
| work_keys_str_mv | AT laceyhelton theisometrictheoryofclassicalbanachspaces |