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Banach Spaces of Analytic Functions and Absolutely Summing Operators
 
A co-publication of the AMS and CBMS
Banach Spaces of Analytic Functions and Absolutely Summing Operators
Softcover ISBN:  978-0-8218-1680-6
Product Code:  CBMS/30
List Price: $27.00
Individual Price: $21.60
eBook ISBN:  978-1-4704-2390-2
Product Code:  CBMS/30.E
List Price: $25.00
Individual Price: $20.00
Softcover ISBN:  978-0-8218-1680-6
eBook: ISBN:  978-1-4704-2390-2
Product Code:  CBMS/30.B
List Price: $52.00 $39.50
Banach Spaces of Analytic Functions and Absolutely Summing Operators
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Banach Spaces of Analytic Functions and Absolutely Summing Operators
A co-publication of the AMS and CBMS
Softcover ISBN:  978-0-8218-1680-6
Product Code:  CBMS/30
List Price: $27.00
Individual Price: $21.60
eBook ISBN:  978-1-4704-2390-2
Product Code:  CBMS/30.E
List Price: $25.00
Individual Price: $20.00
Softcover ISBN:  978-0-8218-1680-6
eBook ISBN:  978-1-4704-2390-2
Product Code:  CBMS/30.B
List Price: $52.00 $39.50
  • Book Details
     
     
    CBMS Regional Conference Series in Mathematics
    Volume: 301977; 91 pp
    MSC: Primary 46; Secondary 30; 32

    This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.

    Readership

  • Table of Contents
     
     
    • Chapters
    • 1. Preface
    • 0. Preliminaries
    • 1. The F. and M. Riesz Theorem and Duals of the Disc Algebra
    • 2. Absolutely Summing Operators from the Disc Algebra
    • 3. Absolutely Summing Operators from the Disc Algebra into Hilbert Space
    • 4. The Nonexistence of Local Unconditional Structure for the Disc Algebra and for its Duals
    • 5. Application to Uniform Algebras
    • 6. Uniformly Peaking Families of Functions in $A$ and $H^{\infty }$. The Havin Lemma
    • 7. Characterizations of Weakly Compact Sets in $L^1/H_0^1$ and in $A^*$
    • 8. Weakly Compact Operators from $A$, $L^1/H_0^1$ and $A^*$ and Complemented Subspaces of These Spaces
    • 9. Complementation of Finite Dimensional Subspaces in $A$, $L^1/H_0^1$ and $H^{\infty }$
    • 10. Bases and the Approximation Property in Some Spaces of Analytic Functions
    • 11. The Polydisc Algebra and the $n$-Ball Algebra, and Their Duals
  • Reviews
     
     
    • An almost complete exposition of the results concerning linear topological properties of Banach spaces of analytic functions (mainly of the disc algebras \(A\) and Hardy spaces \(H^p\)) obtained up to 1975 ... Written by one of the pioneers of the theory discussed, who has contributed very much to it.

      The book is worth reading for anyone who enjoys the interplay between function theory and functional analysis.

      S. V. Kisljakov, Mathematical Reviews
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 301977; 91 pp
MSC: Primary 46; Secondary 30; 32

This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.

Readership

  • Chapters
  • 1. Preface
  • 0. Preliminaries
  • 1. The F. and M. Riesz Theorem and Duals of the Disc Algebra
  • 2. Absolutely Summing Operators from the Disc Algebra
  • 3. Absolutely Summing Operators from the Disc Algebra into Hilbert Space
  • 4. The Nonexistence of Local Unconditional Structure for the Disc Algebra and for its Duals
  • 5. Application to Uniform Algebras
  • 6. Uniformly Peaking Families of Functions in $A$ and $H^{\infty }$. The Havin Lemma
  • 7. Characterizations of Weakly Compact Sets in $L^1/H_0^1$ and in $A^*$
  • 8. Weakly Compact Operators from $A$, $L^1/H_0^1$ and $A^*$ and Complemented Subspaces of These Spaces
  • 9. Complementation of Finite Dimensional Subspaces in $A$, $L^1/H_0^1$ and $H^{\infty }$
  • 10. Bases and the Approximation Property in Some Spaces of Analytic Functions
  • 11. The Polydisc Algebra and the $n$-Ball Algebra, and Their Duals
  • An almost complete exposition of the results concerning linear topological properties of Banach spaces of analytic functions (mainly of the disc algebras \(A\) and Hardy spaces \(H^p\)) obtained up to 1975 ... Written by one of the pioneers of the theory discussed, who has contributed very much to it.

    The book is worth reading for anyone who enjoys the interplay between function theory and functional analysis.

    S. V. Kisljakov, Mathematical Reviews
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.