Abstract
AbstractIt is known that whenever E1, … , En are infinite dimensional L∞‐spaces and F is any infinite dimensional Banach space, there exists a bounded n‐linear mapping from E1 × … × En into F that fails to be absolutely (1; 2)‐summing. In this paper we generalize a theorem of S. Kwapién and obtain a sufficient condition in order to assure that a given n‐linear mapping T from infinite dimensional L∞‐spaces into an infinite dimensional Hilbert space is absolutely (1; 2)‐summing. Besides, we also give a sufficient condition in order to obtain a fully (1; 1)‐summing multilinear mapping from l1 ×…× l1 × l2 into an infinite dimensional Hilbert space. In the last section we introduce the concept of fully summing holomorphic mappings and give the first examples of this kind of map. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
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