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Series in Real Analysis - Vol. 4
LINEAR FUNCTIONAL ANALYSIS
by Wladyslaw Orlicz (Polish Acad. Sci.)
translated from the Chinese edition by Lee Peng Yee (National University of Singapore, Singapore)
with an addendum by Wu Congxin (Harbin Institute of Technology)
Linear Functional Analysis resulted from a series of lectures Orlicz gave in Beijing, China, 1958. The orignal edition was published in Chinese in 1963. It contains all the major theorems that would normally appear in a modern text, the results of special interest to the Polish school, and others which are not easily available elsewhere. Orlicz provided in this book some rare insight and motivation in the subject which was initiated by the Polish school. An addendum to some recent results in Orlicz spaces is included.
Contents:
- Some Preliminaries in Functional Analysis
- Examples of
B-Spaces and F-Spaces
- A Unified Approach of Various Useful B-Spaces and F-Spaces
- Normed Spaces Induced by Given Spaces
- Equivalent Norms, Isomorphism and Isometry of Spaces
- Topological Linear Spaces and Various Concepts of Convergence
- Several Remarks on Different Structures of Spaces of Different Kinds
- Unconditional and Absolute Convergence of Series of Elements
- Linear Functionals on B-Spaces and B0-Spaces
- Several Theorems on Weak Convergence in B-Spaces and B0-Spaces
- Conjugate Spaces of Spaces of Various Types
- On the Continuity of Operators. Various Theorems on Operator Sequences
- Some Applications on Summability Theory and Bi-Orthogonal Expansions
- Exercises
- Bibliography
- Index
Readership: Graduate students in mathematics and mathematicians.
| 264pp |
Pub. date: Jun 1992 |
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