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On summability of bilinear operators
Author(s) -
Carando Daniel,
Dimant Verónica
Publication year - 2003
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.200310090
Subject(s) - mathematics , bilinear interpolation , hilbert space , pure mathematics , operator (biology) , symmetric bilinear form , bilinear map , bilinear form , space (punctuation) , linear map , linguistics , statistics , biochemistry , chemistry , philosophy , repressor , transcription factor , gene
We study some properties of strongly and absolutely p ‐summing bilinear operators. We show that Hilbert‐Schmidt bilinear mappings are both strongly and absolutely p ‐summing, for every p ≥ 1. Giving an example of a strongly 1‐summing bilinear mapping which fails to be weakly compact, we answer a question posed in [6]. We prove that, as in the linear case, every bilinear operator from ℒ ∞ ‐spaces to an ℒ 2 ‐space is absolutely 2‐summing. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)