Skip to main content
SpringerLink
Log in
Birkhäuser
Book cover

Series in Banach Spaces

Conditional and Unconditional Convergence

  • Book
  • © 1997

Overview

Authors:
  1. Mikhail I. Kadets

    1. Kharkov, Ukraine

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Vladimir M. Kadets

    1. Kharkov, Ukraine

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Operator Theory: Advances and Applications (OT, volume 94)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-viii
    Download chapter PDF

  2. Notations

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 1-3

  3. Background Material

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 5-12

  4. Series in a Finite-Dimensional Space

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 13-27

  5. Conditional Convergence in an Infinite-Dimensional Space

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 29-43

  6. Unconditionally Convergent Series

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 45-57

  7. Orlicz’s Theorem and The Structure of Finite-Dimensional Subspaces

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 59-70

  8. Some Results from the General Theory of Banach Spaces

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 71-86

  9. Steinitz’s Theorem and B-Convexity

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 87-100

  10. Rearrangements of Series in Topological Vector Spaces

    • Mikhail I. Kadets, Vladimir M. Kadets
    Pages 101-117

  11. Back Matter

    Pages 119-159
    Download chapter PDF
Back to top

Keywords

About this book

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.

Reviews

“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)

Authors and Affiliations

  • Kharkov, Ukraine

    Mikhail I. Kadets, Vladimir M. Kadets

Bibliographic Information

  • Book Title: Series in Banach Spaces

  • Book Subtitle: Conditional and Unconditional Convergence

  • Authors: Mikhail I. Kadets, Vladimir M. Kadets

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9196-7

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkh�user Verlag 1997

  • Hardcover ISBN: 978-3-7643-5401-5Published: 20 March 1997

  • Softcover ISBN: 978-3-0348-9942-0Published: 11 November 2011

  • eBook ISBN: 978-3-0348-9196-7Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: VIII, 159

  • Topics: Functional Analysis, Analysis, Geometry

Publish with us

Policies and ethics

Back to top

Search

Navigation