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Series in Banach Spaces: Conditional and Unconditional Convergence

By (author) Vladimir Kadets

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normal price: R 4 534.95

Price: R 4 307.95

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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 charÂ 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 unconÂ 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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Helgoland: The Strange and Beautiful Story of Quantum Physics

Carlo Rovelli
Paperback / softback
208 pages
was: R 295.95
now: R 265.95
Available from overseas. Usually dispatched in 3 to 6 weeks

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The Order of Time

Carlo Rovelli
Paperback / softback
224 pages
was: R 295.95
now: R 265.95
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Originally published in Italian: L'ordine del tempo (Milan: Adelphi Edizioni, 2017).

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The Coming Wave: AI, Power and Our Future

Mustafa Suleyman
Paperback / softback
352 pages
was: R 295.95
now: R 265.95
Stock is usually dispatched in 6-12 days from date of order

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