Item description for Infinite Matrices and the Gliding Hump by Charles Swartz...
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 applications 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 Antosik 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 continuity of separately continuous bilinear mappings are also given. Finally, the matrix theorems are also employed to treat a number of topics in sequence spaces.
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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 8.6" Width: 5.9" Height: 0.8" Weight: 0.95 lbs.
Release Date Jan 15, 1996
Publisher World Scientific Publishing Company
ISBN 9810227361 ISBN13 9789810227364
Availability 0 units.
More About Charles Swartz
Charles Swartz was born in 1938 and has an academic affiliation as follows - NMSU-College, Las Cruces, New Mexico, USA.