Multiplier Convergent Series PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Multiplier Convergent Series PDF full book. Access full book title Multiplier Convergent Series by Charles Swartz. Download full books in PDF and EPUB format.
Author: Charles Swartz
Publisher: World Scientific
ISBN: 9812833889
Category : Mathematics
Languages : en
Pages : 264
Get Book Here
Book Description
If ? is a space of scalar-valued sequences, then a series ?j xj in a topological vector space X is ?-multiplier convergent if the series ?j=18 tjxj converges in X for every {tj} e?. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the OrliczOCoPettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical HahnOCoSchur theorem on the equivalence of weak and norm convergent series in ?1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.
Author: Charles Swartz
Publisher: World Scientific
ISBN: 9812833889
Category : Mathematics
Languages : en
Pages : 264
Get Book Here
Book Description
If ? is a space of scalar-valued sequences, then a series ?j xj in a topological vector space X is ?-multiplier convergent if the series ?j=18 tjxj converges in X for every {tj} e?. This monograph studies properties of such series and gives applications to topics in locally convex spaces and vector-valued measures. A number of versions of the OrliczOCoPettis theorem are derived for multiplier convergent series with respect to various locally convex topologies. Variants of the classical HahnOCoSchur theorem on the equivalence of weak and norm convergent series in ?1 are also developed for multiplier convergent series. Finally, the notion of multiplier convergent series is extended to operator-valued series and vector-valued multipliers.
Author: Charles W Swartz
Publisher: World Scientific
ISBN: 9813232781
Category : Mathematics
Languages : en
Pages : 302
Get Book Here
Book Description
The book presents a theory of abstract duality pairs which arises by replacing the scalar field by an Abelian topological group in the theory of dual pair of vector spaces. Examples of abstract duality pairs are vector valued series, spaces of vector valued measures, spaces of vector valued integrable functions, spaces of linear operators and vector valued sequence spaces. These examples give rise to numerous applications such as abstract versions of the Orlicz-Pettis Theorem on subseries convergent series, the Uniform Boundedness Principle, the Banach-Steinhaus Theorem, the Nikodym Convergence theorems and the Vitali-Hahn-Saks Theorem from measure theory and the Hahn-Schur Theorem from summability. There are no books on the current market which cover the material in this book. Readers will find interesting functional analysis and the many applications to various topics in real analysis.
Author: Charles W Swartz
Publisher: World Scientific
ISBN: 9814498718
Category : Mathematics
Languages : en
Pages : 222
Get Book Here
Book 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.
Author: Juan Carlos Navarro Pascual
Publisher: World Scientific
ISBN: 9814699705
Category : Mathematics
Languages : en
Pages : 319
Get Book Here
Book Description
This volume contains recent papers by several specialists in different fields of mathematical analysis. It offers a reasonably wide perspective of the current state of research, and new trends, in areas related to measure theory, harmonic analysis, non-associative structures in functional analysis and summability in locally convex spaces.Those interested in researching any areas of mathematical analysis will find here numerous suggestions on possible topics with an important impact today. Often, the contributions are presented in an expository nature and this makes the discussed topics accessible to a more general audience.
Author: Piotr Antosik
Publisher: Springer
ISBN: 3540392661
Category : Mathematics
Languages : en
Pages : 118
Get Book Here
Book Description
Author: Vicente Montesinos
Publisher: Springer
ISBN: 3319124811
Category : Mathematics
Languages : en
Pages : 884
Get Book Here
Book Description
Examining the basic principles in real analysis and their applications, this text provides a self-contained resource for graduate and advanced undergraduate courses. It contains independent chapters aimed at various fields of application, enhanced by highly advanced graphics and results explained and supplemented with practical and theoretical exercises. The presentation of the book is meant to provide natural connections to classical fields of applications such as Fourier analysis or statistics. However, the book also covers modern areas of research, including new and seminal results in the area of functional analysis.
Author: Sociedad Matemática Mexicana
Publisher:
ISBN:
Category : Mathematics
Languages : en
Pages : 648
Get Book Here
Book Description
Author: Antonio Boccuto
Publisher: Bentham Science Publishers
ISBN: 1681080095
Category : Mathematics
Languages : en
Pages : 548
Get Book Here
Book Description
Convergence Theorems for Lattice Group-valued Measures explains limit and boundedness theorems for measures taking values in abstract structures. The book begins with a historical survey about these topics since the beginning of the last century, moving on to basic notions and preliminaries on filters/ideals, lattice groups, measures and tools which are featured in the rest of this text. Readers will also find a survey on recent classical results about limit, boundedness and extension theorems for lattice group-valued measures followed by information about recent developments on these kinds of theorems and several results in the setting of filter/ideal convergence. In addition, each chapter has a general description of the topics and an appendix on random variables, concepts and lattices is also provided. Thus readers will benefit from this book through an easy-to-read historical survey about all the problems on convergence and boundedness theorems, and the techniques and tools which are used to prove the main results. The book serves as a primer for undergraduate, postgraduate and Ph. D. students on mathematical lattice and topological groups and filters, and a treatise for expert researchers who aim to extend their knowledge base.
Author:
Publisher:
ISBN:
Category : Mathematical analysis
Languages : en
Pages : 1084
Get Book Here
Book Description
Author: Piotr Antosik
Publisher: World Scientific Publishing Company
ISBN:
Category : Mathematics
Languages : en
Pages : 404
Get Book Here
Book Description
The conference was devoted to the memory of the late Professor Jan Mikusinski. The proceedings is divided into three parts. The first one contains biographical materials and memoirs about Professor Mikusinski and his work. The second part is devoted to the theory of generalized functions and the third to convergence structures.
