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Banach Spaces of Analytic Functions and Absolutely Summing Operators

About this Title

A. Pelczynski

Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 1977; Volume 30
ISBNs: 978-0-8218-1680-6 (print); 978-1-4704-2390-2 (online)
DOI: https://doi.org/10.1090/cbms/030

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Table of Contents

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Front/Back Matter

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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