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Series in Banach Spaces: Conditional and Unconditional Convergence (Operator Theory: Advances and Applications, 94) - Hardcover
Synopsis
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 series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements.
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Language Notes
Text: English (translation)
Original Language: Russian
Review
“The material in the book is always started with motivation. There are plenty of exercises, with hints for solution. The list of references is complete and up-to-day. This is an amazing book on doctoral level, written by experienced authors, who contributed a lot to the subject presented in the book.” (J.Musielak, zbMATH, 0876.46009, 1997)
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Series in Banach Spaces: Conditional and Unconditional Convergence (Operator Theory: Advances and Applications, 94)
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Series in Banach Spaces
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Series in Banach Spaces
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Springer, Basel, Birkhäuser Basel, Birkhäuser Mrz 1997, 1997
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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 series converges only for certain rearrangements of its terms (in other words, converges conditionally), to describe its sum range, i.e., the set of sums of all its convergent rearrangements. 159 pp. Englisch. Seller Inventory # 9783764354015
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Series in Banach Spaces
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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 ser. Seller Inventory # 5279125
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Series in Banach Spaces
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Condition: New. The beautiful Riemann theorem states that a series can change its sum after permutation of the terms. This work contains many exercises and unsolved problems as well as an appendix about the problems in vector-valued Riemann integration. It is suitable for graduate students and mathematicians interested in functional analysis. Series: Operator Theory: Advances and Applications. Num Pages: 167 pages, biography. BIC Classification: PBKF; PBM; PBP. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 234 x 156 x 11. Weight in Grams: 930. . 1997. Hardback. . . . . Seller Inventory # V9783764354015
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Series in Banach Spaces
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Series in Banach Spaces: Conditional and Unconditional Convergence (Operator Theory: Advances and Applications, 94)
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