History Of Banach Spaces And Linear Operators


History Of Banach Spaces And Linear Operators
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History Of Banach Spaces And Linear Operators


History Of Banach Spaces And Linear Operators
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Author : Albrecht Pietsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-31

History Of Banach Spaces And Linear Operators written by Albrecht Pietsch 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 2007-12-31 with Mathematics categories.


Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.



History Of Banach Spaces And Linear Operators


History Of Banach Spaces And Linear Operators
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Author : Albrecht Pietsch
language : en
Publisher:
Release Date : 2003

History Of Banach Spaces And Linear Operators written by Albrecht Pietsch and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with categories.




Theory Of Linear Operations


Theory Of Linear Operations
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Author : S. Banach
language : en
Publisher: Elsevier
Release Date : 1987-03-01

Theory Of Linear Operations written by S. Banach and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-03-01 with Computers categories.


This classic work by the late Stefan Banach has been translated into English so as to reach a yet wider audience. It contains the basics of the algebra of operators, concentrating on the study of linear operators, which corresponds to that of the linear forms a1x1 + a2x2 + ... + anxn of algebra. The book gathers results concerning linear operators defined in general spaces of a certain kind, principally in Banach spaces, examples of which are: the space of continuous functions, that of the pth-power-summable functions, Hilbert space, etc. The general theorems are interpreted in various mathematical areas, such as group theory, differential equations, integral equations, equations with infinitely many unknowns, functions of a real variable, summation methods and orthogonal series. A new fifty-page section (``Some Aspects of the Present Theory of Banach Spaces'') complements this important monograph.



Trends In Banach Spaces And Operator Theory


Trends In Banach Spaces And Operator Theory
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Author : Anna Kamińska
language : en
Publisher: American Mathematical Soc.
Release Date : 2003

Trends In Banach Spaces And Operator Theory written by Anna Kamińska and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.


This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.



Factorization Of Linear Operators And Geometry Of Banach Spaces


Factorization Of Linear Operators And Geometry Of Banach Spaces
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Author : Gilles Pisier
language : en
Publisher: American Mathematical Soc.
Release Date : 1986

Factorization Of Linear Operators And Geometry Of Banach Spaces written by Gilles Pisier and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.


"Expository lectures from the CBMS regional conference held at the University of Missouri-Columbia, June 25-29, 1984"--T.p. verso.



Denseness Bases And Frames In Banach Spaces And Applications


Denseness Bases And Frames In Banach Spaces And Applications
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Author : Aref Jeribi
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-03-19

Denseness Bases And Frames In Banach Spaces And Applications written by Aref Jeribi and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-19 with Mathematics categories.


This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory



Basic Classes Of Linear Operators


Basic Classes Of Linear Operators
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Author : Israel Gohberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-10-24

Basic Classes Of Linear Operators written by Israel Gohberg 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 2003-10-24 with Mathematics categories.


A comprehensive graduate textbook that introduces functional analysis with an emphasis on the theory of linear operators and its application to differential equations, integral equations, infinite systems of linear equations, approximation theory, and numerical analysis. As a textbook designed for senior undergraduate and graduate students, it begins with the geometry of Hilbert spaces and proceeds to the theory of linear operators on these spaces including Banach spaces. Presented as a natural continuation of linear algebra, the book provides a firm foundation in operator theory which is an essential part of mathematical training for students of mathematics, engineering, and other technical sciences.



Interpolation Of Linear Operators


Interpolation Of Linear Operators
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Author : S. G. Krein
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-10-21

Interpolation Of Linear Operators written by S. G. Krein and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-21 with Mathematics categories.




The Asymptotic Behaviour Of Semigroups Of Linear Operators


The Asymptotic Behaviour Of Semigroups Of Linear Operators
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Author : Jan van Neerven
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06

The Asymptotic Behaviour Of Semigroups Of Linear Operators written by Jan van Neerven and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.


This book presents a systematic account of the theory of asymptotic behaviour of semigroups of linear operators acting in a Banach space. The focus is on the relationship between asymptotic behaviour of the semigroup and spectral properties of its infinitesimal generator. The most recent developments in the field are included, such as the Arendt-Batty-Lyubich-Vu theorem, the spectral mapp- ing theorem of Latushkin and Montgomery-Smith, Weis's theorem on stability of positive semigroup in Lp-spaces, the stability theorem for semigroups whose resolvent is bounded in a half-plane, and a systematic theory of individual stability. Addressed to researchers and graduate students with interest in the fields of operator semigroups and evolution equations, this book is self-contained and provides complete proofs.



Introduction To Operator Theory In Riesz Spaces


Introduction To Operator Theory In Riesz Spaces
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Author : Adriaan C. Zaanen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Introduction To Operator Theory In Riesz Spaces written by Adriaan C. Zaanen 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.


Since the beginning of the thirties a considerable number of books on func tional analysis has been published. Among the first ones were those by M. H. Stone on Hilbert spaces and by S. Banach on linear operators, both from 1932. The amount of material in the field of functional analysis (in cluding operator theory) has grown to such an extent that it has become impossible now to include all of it in one book. This holds even more for text books. Therefore, authors of textbooks usually restrict themselves to normed spaces (or even to Hilbert space exclusively) and linear operators in these spaces. In more advanced texts Banach algebras and (or) topological vector spaces are sometimes included. It is only rarely, however, that the notion of order (partial order) is explicitly mentioned (even in more advanced exposi tions), although order structures occur in a natural manner in many examples (spaces of real continuous functions or spaces of measurable function~). This situation is somewhat surprising since there exist important and illuminating results for partially ordered vector spaces, in . particular for the case that the space is lattice ordered. Lattice ordered vector spaces are called vector lattices or Riesz spaces. The first results go back to F. Riesz (1929 and 1936), L. Kan torovitch (1935) and H. Freudenthal (1936).