Linear Functional Analysis

By: Peng Yee Lee, Cong Xin Wu

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Hardcover | 1 December 1991

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264 Pages

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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.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Real Analysis Differential Calculus & Equations Booktopia Publisher Services World Scientific Publishing

Preface
Chinese translator's preface
Preface to the chinese edition
Acknowledgement
Some preliminaries in functional analysis	p. 1
Examples of B-spaces and F-spaces	p. 6
A unified approach of various useful B-spaces and F-spaces	p. 11
Normed spaces induced by given spaces	p. 24
Equivalent norms, isomorphism and isometry of spaces	p. 32
Topological linear spaces and various concepts of convergence	p. 37
Several remarks on different structures of spaces of different kinds	p. 50
Unconditional and absolute convergence of series of elements	p. 53
Linear functionals on B-spaces and B[subscript 0]-spaces	p. 63
Several theorems on weak convergence in B-spaces and B[subscript 0]-spaces	p. 90
Conjugate spaces of spaces of various types	p. 102
On the continuity of operators. Various theorems on operator sequences	p. 121
Some applications on summability theory and bi-orthogonal expansions	p. 136
Addendum: Some results in Orlicz spaces
A formula for Orlicz norm and its applications	p. 153
Bounded linear functionals on the Orlicz space and smoothness	p. 163
Integral operators on the Orlicz spaces	p. 170
Orlicz sequence spaces and Orlicz-Musielak sequence spaces	p. 178
Generalized Orlicz spaces L[actual symbols not reproducible][a,b]	p. 186
Orthogonally additive functionals	p. 195
The significance of Orlicz spaces	p. 203
Exercises	p. 211
Bibliography	p. 237
Index	p. 244
Table of Contents provided by Blackwell. All Rights Reserved.

Linear Functional Analysis

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