Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 61, No. 1, pp. 25-33 (2004)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home



Bounded holomorphic mappings and the compact approximation property in Banach spaces

Erhan Çal\iskan

Departamento de Matemática e Estatística, Universidade Federal de Campina Grande,
Caixa Postal 10044, Bodocongó, CEP 58109-970 Campina Grande, PB -- BRAZIL
E-mail: caliskan@dme.ufcg.edu.br

Abstract: We study the compact approximation property in connection with the space of bounded holomorphic mappings on a Banach space. When $U$ is a bounded balanced open subset of a Banach space $E$, we show that the predual of the space of the bounded holomorphic functions on $U$, $G^{\infty}(U)$, has the compact approximation property if and only if $E$ has the compact approximation property. We also show that $E$ has the compact approximation property if and only if each continuous Banach-valued polynomial on $E$ can be uniformly approximated on compact sets by polynomials which are weakly continuous on bounded sets.

Keywords: Banach spaces; compact approximation property; bounded holomorphic functions.

Classification (MSC2000): 46G20, 46B28, 46G25.

Full text of the article:

Electronic version published on: 7 Mar 2008.

© 2004 Sociedade Portuguesa de Matemática
© 2004–2008 ELibM and FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition