Linear Functional Analysis

by Lee Peng Yee, Cong Xin Wu

With an addendum by WuCongxin ("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 AnalysisExamples of "B"-Spaces and "F"-SpacesA Unified Approach of Various Useful "B"-Spaces and "F"-SpacesNormed Spaces Induced by Given SpacesEquivalent Norms, Isomorphism and Isometry of SpacesTopological Linear Spaces and Various Concepts of ConvergenceSeveral Remarks on Different Structures of Spaces of Different KindsUnconditional and Absolute Convergence of Series of ElementsLinear Functionals on "B"-Spaces and "B"0-SpacesSeveral Theorems on Weak Convergence in "B"-Spaces and "B"0-SpacesConjugate Spaces of Spaces of Various TypesOn the Continuity of Operators. Various Theorems on Operator SequencesSome Applications on Summability Theory and Bi-Orthogonal ExpansionsExercisesBibliographyIndex
Readership: Graduate students in mathematics and mathematicians.

266 pages, ebook

First published January 1, 1992