Bourgain, J. New Banach space properties of certain spaces of analytic functions. (English) Zbl 0592.46048 Proc. Int. Congr. Math., Warszawa 1983, Vol. 2, 945-951 (1984). [For the entire collection see Zbl 0553.00001.] This report is a survey on the isomorphic theory of spaces of analytic functions, specially the disc algebra A(D) and related topics. Most of the contents is dedicated to results of the author. Open and recently solved problems on local structure, isomorphic classification, interpolation and approximation in certain algebras of analytic functions in several variables are considered. Reviewer: G.López Lagomasino MSC: 46J15 Banach algebras of differentiable or analytic functions, \(H^p\)-spaces 41A05 Interpolation in approximation theory 41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) Keywords:isomorphic theory of spaces of analytic functions; disc algebra; local structure; isomorphic classification; interpolation; approximation Citations:Zbl 0553.00001 PDFBibTeX XML