Counterexamples In Topological Vector Spaces

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Counterexamples In Topological Vector Spaces

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Author : S. M. Khaleelulla
language : en
Publisher:
Release Date : 2014-01-15

Counterexamples In Topological Vector Spaces written by S. M. Khaleelulla and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Counterexamples In Topological Vector Spaces

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Author : S.M. Khaleelulla
language : en
Publisher: Springer
Release Date : 2006-11-17

Counterexamples In Topological Vector Spaces written by S.M. Khaleelulla and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-17 with Mathematics categories.

Semitopological Vector Spaces

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Author : Mark Burgin
language : en
Publisher: CRC Press
Release Date : 2017-06-26

Semitopological Vector Spaces written by Mark Burgin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-26 with Mathematics categories.

This new volume shows how it is possible to further develop and essentially extend the theory of operators in infinite-dimensional vector spaces, which plays an important role in mathematics, physics, information theory, and control theory. The book describes new mathematical structures, such as hypernorms, hyperseminorms, hypermetrics, semitopological vector spaces, hypernormed vector spaces, and hyperseminormed vector spaces. It develops mathematical tools for the further development of functional analysis and broadening of its applications. Exploration of semitopological vector spaces, hypernormed vector spaces, hyperseminormed vector spaces, and hypermetric vector spaces is the main topic of this book. A new direction in functional analysis, called quantum functional analysis, has been developed based on polinormed and multinormed vector spaces and linear algebras. At the same time, normed vector spaces and topological vector spaces play an important role in physics and in control theory. To make this book comprehendible for the reader and more suitable for students with some basic knowledge in mathematics, denotations and definitions of the main mathematical concepts and structures used in the book are included in the appendix, making the book useful for enhancing traditional courses of calculus for undergraduates, as well as for separate courses for graduate students. The material of Semitopological Vector Spaces: Hypernorms, Hyperseminorms and Operators is closely related to what is taught at colleges and universities. It is possible to use a definite number of statements from the book as exercises for students because their proofs are not given in the book but left for the reader.

Probability Theory On Vector Spaces Iii

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Author : D Szynal
language : en
Publisher: Springer
Release Date : 2006-12-08

Probability Theory On Vector Spaces Iii written by D Szynal and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.

Counterexamples To Probl Me Des Topologies Of Grothendieck

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Author : Jari Taskinen
language : en
Publisher:
Release Date : 1986

Counterexamples To Probl Me Des Topologies Of Grothendieck written by Jari Taskinen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Linear topological spaces categories.

Counterexamples In Probability And Statistics

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Author : A.F. Siegel
language : en
Publisher: Routledge
Release Date : 2017-11-22

Counterexamples In Probability And Statistics written by A.F. Siegel and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

This volume contains six early mathematical works, four papers on fiducial inference, five on transformations, and twenty-seven on a miscellany of topics in mathematical statistics. Several previously unpublished works are included.

Topological Vector Spaces

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Author : Norbert Adasch
language : en
Publisher: Springer
Release Date : 2006-11-15

Topological Vector Spaces written by Norbert Adasch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

The first five sections deliver the general setting of the theory (topological vector spaces, metrizability, projective and inductive limits, topological direct sums). In sections 6-10 we investigate the class of "barrelled" topological vector spaces which is important also in this general theory. The main part of these sections is take by theorems on linear mappings (the Banach-Steinhaus theorem, closed graph theorems, open mapping theorems). Section 11 introduces the "bornological" spaces, and in section 12 we deal with spaces of linear mappings and their topologies. Interesting generalizations of the class of (DF)-spaces are given in sections 15-17 by considering the following property: a subset, which is "large enough", is a neighborhood of 0, if and only if it includes a neighborhood on all bounded balanced sets. Finally, section 18 interprets and completes the foregoing considerations for (DF)-spaces.

Topological Vector Spaces I

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Author : Gottfried Köthe
language : en
Publisher: CUP Archive
Release Date : 1983

Topological Vector Spaces I written by Gottfried Köthe and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.

It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.

Infinite Matrices And The Gliding Hump Matrix Methods In Analysis

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Author : Charles W Swartz
language : en
Publisher: World Scientific
Release Date : 1996-08-22

Infinite Matrices And The Gliding Hump Matrix Methods In Analysis written by Charles W Swartz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-08-22 with Mathematics categories.

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.

Clifford Algebras With Numeric And Symbolic Computations

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Author : Rafal Ablamowicz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Clifford Algebras With Numeric And Symbolic Computations written by Rafal Ablamowicz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Clifford algebras are at a crossing point in a variety of research areas, including abstract algebra, crystallography, projective geometry, quantum mechanics, differential geometry and analysis. For many researchers working in this field in ma- thematics and physics, computer algebra software systems have become indispensable tools in theory and applications. This edited survey book consists of 20 chapters showing application of Clifford algebra in quantum mechanics, field theory, spinor calculations, projective geometry, Hypercomplex algebra, function theory and crystallography. Many examples of computations performed with a variety of readily available software programs are presented in detail, i.e., Maple, Mathematica, Axiom, etc. A key feature of the book is that it shows how scientific knowledge can advance with the use of computational tools and software.