Infinite Matrices and the Gliding Hump Издательство: World Scientific Publishing Company, 1996 г Твердый переплет, 210 стр ISBN 9810227361 Язык: Английский инфо 11826i.

These notes present a theorem on infinite matrices with values in a topological group due to P Antosik and J Mikusinski Using the matrix theorem and classical gliding hump techniques, a number of applicationsаюхут to various topics in functional analysis, measure theory and sequence spaces are given There are a number of generalizations of the classical Uniform Boundedness Principle given; in particular, using stronger notions of sequential convergence and boundedness due to Aбмлбтntosik and Mikusinski, versions of the Uniform Boundedness Principle and the Banach-Steinhaus Theorem are given which, in contrast to the usual versions, require no completeness or barrelledness assumptions on the domain space Versions of Nikodym Boundedness and Convergence Theorems of measure theory, the Orlicz-Pettis Theorem on subseries convergence, generalizations of the Schur Lemma on the equivalence of weak and norm convergence in l1 and the Mazur-Orlicz Theorem on the continuiбспынty of separately continuous bilinear mappings are also given Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces 1st edition Автор Charles Swartz.

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