Banach Spaces of Analytic Functions and Absolutely Summing Operators

Abstract

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.