The bounded approximation property for weakly uniformly continuous type holomorphic mappings

Abstract

When 𝑈 is a balanced open subset of a reflexive Banach space 𝐸 with 𝑃 (ⁿ 𝐸) = Pw(ⁿ 𝐸) for every positive integer 𝑛, we show that the predual of the space of weakly uniformly continuous holomorphic mappings on 𝑈, 𝐺wu(𝑈), has the bounded approximation property if and only if 𝐸 has the bounded approximation property if and only if 𝑃(ⁿ𝐸) has the bounded approximation property for every positive integer 𝑛. An analogous result is established for the predual of the space of holomorphic mappings of bounded type also. Key words: Banach spaces, locally convex spaces, bounded approximation property, holomorphic mappings of bounded type, weakly uniformly continuous functions, bounded holomorphic mappings.