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Rearrangements of Series in Banach Spaces
 
Rearrangements of Series in Banach Spaces
Hardcover ISBN:  978-0-8218-4546-2
Product Code:  MMONO/86
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4498-3
Product Code:  MMONO/86.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4546-2
eBook: ISBN:  978-1-4704-4498-3
Product Code:  MMONO/86.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
Rearrangements of Series in Banach Spaces
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Rearrangements of Series in Banach Spaces
Hardcover ISBN:  978-0-8218-4546-2
Product Code:  MMONO/86
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
eBook ISBN:  978-1-4704-4498-3
Product Code:  MMONO/86.E
List Price: $155.00
MAA Member Price: $139.50
AMS Member Price: $124.00
Hardcover ISBN:  978-0-8218-4546-2
eBook ISBN:  978-1-4704-4498-3
Product Code:  MMONO/86.B
List Price: $320.00 $242.50
MAA Member Price: $288.00 $218.25
AMS Member Price: $256.00 $194.00
  • Book Details
     
     
    Translations of Mathematical Monographs
    Volume: 861991; 123 pp
    MSC: Primary 46;

    In a contemporary course in mathematical analysis, the concept of series arises as a natural generalization of the concept of a sum over finitely many elements, and the simplest properties of finite sums carry over to infinite series. Standing as an exception among these properties is the commutative law, for the sum of a series can change as a result of a rearrangement of its terms. This raises two central questions: for which series is the commutative law valid, and just how can a series change upon rearrangement of its terms? Both questions have been answered for all finite-dimensional spaces, but the study of rearrangements of a series in an infinite-dimensional space continues to this day.

    In recent years, a close connection has been discovered between the theory of series and the so-called finite properties of Banach spaces, making it possible to create a unified theory from the numerous separate results. This book is the first attempt at such a unified exposition.

    This book would be an ideal textbook for advanced courses, for it requires background only at the level of standard courses in mathematical analysis and linear algebra and some familiarity with elementary concepts and results in the theory of Banach spaces. The authors present the more advanced results with full proofs, and they have included a large number of exercises of varying difficulty. A separate section in the last chapter is devoted to a detailed survey of open questions. The book should prove useful and interesting both to beginning mathematicians and to specialists in functional analysis.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Chapter 1. General information
    • Chapter 2. Conditionally convergent series
    • Chapter 3. Unconditionally convergent series
    • Chapter 4. Some results in the general theory of Banach spaces
    • Chapter 5. $M$-cotype and the Orlicz theorem
    • Chapter 6. The Steinitz theorem and $B$-convexity
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 861991; 123 pp
MSC: Primary 46;

In a contemporary course in mathematical analysis, the concept of series arises as a natural generalization of the concept of a sum over finitely many elements, and the simplest properties of finite sums carry over to infinite series. Standing as an exception among these properties is the commutative law, for the sum of a series can change as a result of a rearrangement of its terms. This raises two central questions: for which series is the commutative law valid, and just how can a series change upon rearrangement of its terms? Both questions have been answered for all finite-dimensional spaces, but the study of rearrangements of a series in an infinite-dimensional space continues to this day.

In recent years, a close connection has been discovered between the theory of series and the so-called finite properties of Banach spaces, making it possible to create a unified theory from the numerous separate results. This book is the first attempt at such a unified exposition.

This book would be an ideal textbook for advanced courses, for it requires background only at the level of standard courses in mathematical analysis and linear algebra and some familiarity with elementary concepts and results in the theory of Banach spaces. The authors present the more advanced results with full proofs, and they have included a large number of exercises of varying difficulty. A separate section in the last chapter is devoted to a detailed survey of open questions. The book should prove useful and interesting both to beginning mathematicians and to specialists in functional analysis.

  • Chapters
  • Introduction
  • Chapter 1. General information
  • Chapter 2. Conditionally convergent series
  • Chapter 3. Unconditionally convergent series
  • Chapter 4. Some results in the general theory of Banach spaces
  • Chapter 5. $M$-cotype and the Orlicz theorem
  • Chapter 6. The Steinitz theorem and $B$-convexity
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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