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|Type:||Artigo de periódico|
|Title:||On a question of Pietsch about Hilbert-Schmidt multilinear mappings|
|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.|
|Editor:||Academic Press Inc|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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