6533b831fe1ef96bd1298d31

RESEARCH PRODUCT

Fréchet Spaces of Holomorphic Functions without Copies of l 1

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Let X be a Banach space. Let Hw*(X*) the Frechet space whose elements are the holomorphic functions defined on X* whose restrictions to each multiple mB(X*), m = 1,2, …, of the closed unit ball B(X*) of X* are continuous for the weak-star topology. A fundamental system of norms for this space is the supremum of the absolute value of each element of Hw*(X*) in mB(X*), m = 1,2,…. In this paper we construct the bidual of l1 when this space contains no copy of l1. We also show that if X is an Asplund space, then Hw*(X*) can be represented as the projective limit of a sequence of Banach spaces that are Asplund.