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Fully summingmultilinear and holomorphicmappings into Hilbert spaces
Author(s) -
Pellegrino Daniel,
Souza Marcela
Publication year - 2005
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200310279
Subject(s) - mathematics , hilbert space , multilinear map , holomorphic function , banach space , bounded function , pure mathematics , order (exchange) , absolute continuity , section (typography) , space (punctuation) , mathematical analysis , discrete mathematics , linguistics , philosophy , business , advertising , finance , economics
It is known that whenever E 1 , … , E n are infinite dimensional L ∞ ‐spaces and F is any infinite dimensional Banach space, there exists a bounded n ‐linear mapping from E 1 × … × E n 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 l 1 ×…× l 1 × l 2 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)