CBMS Regional Conference Series in Mathematics 1977; 91 pp; softcover Number: 30 Reprint/Revision History: fifth printing 1998 ISBN10: 0821816802 ISBN13: 9780821816806 List Price: US$23 Member Price: US$18.40 All Individuals: US$18.40 Order Code: CBMS/30
 This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments. Readership 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 Table of Contents  Preliminaries
 The F. and M. Riesz theorem and duals of the disc algebra
 Absolutely summing operators from the disc algebra
 Absolutely summing operators from the disc algebra into Hilbert space
 The nonexistence of local unconditional structure for the disc algebra and for its duals
 Application to uniform algebras
 Uniformly peaking families of functions in \(A\) and \(H^\infty\). The Havin lemma
 Characterizations of weakly compact sets in \(L^1/H^1_0\) and in \(A^*\)
 Weakly compact operators from \(A\), \(L^1/H^1_0\) and \(A^*\) and complemented subspaces of these spaces
 Complementation of finite dimensional subspaces in \(A\), \(L^1/H^1_0\) and <\(H^\infty\)
 Bases and the approximation property in some spaces of analytic functions
 The polydisc algebra and the \(n\)ball algebra, and their duals
 References
