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Type: Artigo de periódico
Title: On a question of Pietsch about Hilbert-Schmidt multilinear mappings
Author: Matos, MC
Abstract: In 1983, Pietsch asked if, for n greater than or equal to 3 and all Hilbert spaces E-1,..., E-n, the vector space of the scalar valued absolutely (r;r(1),..., r(n))-summing multilinear mappings on E-1 x ... x E-n coincides with the vector space of the n-linear Hilbert-Schmidt functionals on E-1 x...x E-n, for some choice of r, r(1),..., r(n) is an element of ]0, +infinity], satisfying 1/r less than or equal to 1/r(1) + ... + 1/r(n). We show that the answer to this question is no. Moreover, we show that the same question, for n greater than or equal to 2 and mappings with values in infinite dimensional Hilbert spaces, has the answer no. (C) 2001 Academic Press.
Country: EUA
Editor: Academic Press Inc
Citation: Journal Of Mathematical Analysis And Applications. Academic Press Inc, v. 257, n. 2, n. 343, n. 355, 2001.
Rights: fechado
Identifier DOI: 10.1006/jmaa.2000.7351
Date Issue: 2001
Appears in Collections:Unicamp - Artigos e Outros Documentos

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