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Titlebook: Series in Banach Spaces; Conditional and Unco Mikhail I. Kadets,Vladimir M. Kadets Book 1997 Birkh�user Verlag 1997 Finite.Functional analy

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发表于 2025-3-21 16:26:09 | 显示全部楼层 |阅读模式
书目名称Series in Banach Spaces
副标题Conditional and Unco
编辑Mikhail I. Kadets,Vladimir M. Kadets
视频video
丛书名称Operator Theory: Advances and Applications
图书封面Titlebook: Series in Banach Spaces; Conditional and Unco Mikhail I. Kadets,Vladimir M. Kadets Book 1997 Birkh�user Verlag 1997 Finite.Functional analy
描述Series of scalars, vectors, or functions are among the fundamental objects of mathematical analysis. When the arrangement of the terms is fixed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearrangements (permutations) of the terms of a series, which brings combinatorial considerations into the problems studied. The phenomenon that a numerical series can change its sum when the order of its terms is changed is one of the most impressive facts encountered in a university analysis course. The present book is devoted precisely to this aspect of the theory of series whose terms are elements of Banach (as well as other topological linear) spaces. The exposition focuses on two complementary problems. The first is to char­ acterize those series in a given space that remain convergent (and have the same sum) for any rearrangement of their terms; such series are usually called uncon­ ditionally convergent. The second problem is, when a seri
出版日期Book 1997
关键词Finite; Functional analysis; Topology; calculus; function; metrizable; proof; theorem
版次1
doihttps://doi.org/10.1007/978-3-0348-9196-7
isbn_softcover978-3-0348-9942-0
isbn_ebook978-3-0348-9196-7Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightBirkh�user Verlag 1997
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发表于 2025-3-21 23:31:10 | 显示全部楼层
,Orlicz’s Theorem and The Structure of Finite-Dimensional Subspaces,s follows a certain theorem on series in an infinite-dimensional space. Since any finite set of elements lies in some finite-dimensional subspace, in all such assertions only special features of the structure of the finite-dimensional subspaces of the ambient infinite-dimensional space considered pl
发表于 2025-3-22 01:39:49 | 显示全部楼层
Some Results from the General Theory of Banach Spaces,with nonlinear sum range, we need two theorems on the structure of infinite-dimensional spaces: Dvoretzky’s theorem on almost-Euclidean sections and Mazur’s theorem on basic sequences. Since these deep results are not incorporated in the standard functional analysis courses, their proof will be prov
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Rearrangements of Series in Topological Vector Spaces,o sections we construct a number of counterexamples, and in the third section we give a result of W. Banaszczyk which extends Steinitz’s theorem from finite-dimensional spaces to nuclear Fréchet spaces.
发表于 2025-3-22 20:38:20 | 显示全部楼层
0255-0156 xed, investigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one consid
发表于 2025-3-23 01:02:46 | 显示全部楼层
Book 1997tigating a series amounts to investigating the sequence of its partial sums. In this case the theory of series is a part of the theory of sequences, which deals with their convergence, asymptotic behavior, etc. The specific character of the theory of series manifests itself when one considers rearra
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Mikhail I. Kadets,Vladimir M. Kadetskrankungen.Systematische Anleitung zu einem individuell ange.Mit diesem Ratgeber steht dem herzkranken Patienten eine praktische, die ärztlichen Empfehlungen begleitende Anleitung zur Bewegungstherapie zur Verfügung. Körperliche Bewegung und gesunde Lebensweise gehören zusammen. Deshalb informiert d
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