Read Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis

Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis

Charles W. Swartz

4.9/5 (29175 ratings)

Description: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.Contents: IntroductionThe Antosik-Mikusinski Matrix Theoremk-Convergence and k-BoundednessThe Uniform Boundedness PrincipleThe Banach-Steinhaus TheoremContinuity and Hypocontinuity for Bilinear MapsPap's Adjoint TheoremVector Versions of the Hahn-Schur TheoremsAn Abstract Hahn-Schur TheoremThe Orlicz-Pettis TheoremImbedding "c"0 and "l"∞Sequence SpacesReadership: Graduate students in pure mathematics.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis. To get started finding Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: 222

Format: PDF, EPUB & Kindle Edition

Publisher: World Scientific Publishing Company

Release: 2013

ISBN: 1299662587

Description: 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.Contents: IntroductionThe Antosik-Mikusinski Matrix Theoremk-Convergence and k-BoundednessThe Uniform Boundedness PrincipleThe Banach-Steinhaus TheoremContinuity and Hypocontinuity for Bilinear MapsPap's Adjoint TheoremVector Versions of the Hahn-Schur TheoremsAn Abstract Hahn-Schur TheoremThe Orlicz-Pettis TheoremImbedding "c"0 and "l"∞Sequence SpacesReadership: Graduate students in pure mathematics.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis. To get started finding Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis, you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Special Offer | $0.00

Special Offer! | $0.00

Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis

Infinite Matrices and the Gliding Hump, Matrix Methods in Analysis

More Books

Global Initiatives to Secure Cyberspace

Global Initiatives to Secure Cyberspace

Infinite Matrices and Their Recent Applications

Infinite Matrices and Their Recent Applications

Infinite Matrices and their Finite Sections

Infinite Matrices and their Finite Sections

Iterated Function Systems, Moments, and Transformations of Infinite Matrices

Iterated Function Systems, Moments, and Transformations of Infinite Matrices

Infinite Matrices and Sequence Spaces

Infinite Matrices and Sequence Spaces

Infinite Matrices of Operators

Infinite Matrices of Operators

Infinite Matrices and the Gliding Hump

Infinite Matrices and the Gliding Hump

Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices

Limit Operators, Collective Compactness, and the Spectral Theory of Infinite Matrices

Summability Theory and Its Applications

Summability Theory and Its Applications