An F-space sampler
著者
書誌事項
An F-space sampler
（London Mathematical Society lecture note series, 89）
Cambridge University Press, 1984
- : pbk.
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注記
Bibliography: p. 226-237
内容説明・目次
内容説明
This book presents a theory motivated by the spaces LP, 0 p < l. These spaces are not locally convex, so the methods usually encountered in linear analysis (particularly the Hahn-Banach theorem) do not apply here. Questions about the size of the dual space are especially important in the non-locally convex setting, and are a central theme. Several of the classical problems in the area have been settled in the last decade, and a number of their solutions are presented here. The book begins with concrete examples (lp, LP, L0, HP) before going on to general results and important counterexamples. An F-space sampler will be of interest to research mathematicians and graduate students in functional analysis.
目次
- 1. Preliminaries
- 2. Some of the classic results
- 3. Hardy spaces
- 4. The Hahn-Banach extension property
- 5. Three space problems
- 6. Lifting Theorems
- 7. Transitive spaces and small operators
- 8. Operators between LP spaces
- 9. Compact convex sets with no extreme points
- 10. Notes on other directions of research.
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