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On summability of bilinear operators

✍ Scribed by Daniel Carando; Verónica Dimant

Publisher
John Wiley and Sons
Year
2003
Tongue
English
Weight
155 KB
Volume
259
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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 ℒ︁~∞~‐spaces to an ℒ︁~2~‐space is absolutely 2‐summing. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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