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Extension of bilinear forms on Banach spaces

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Castillo, Jesús M.F. and García, R. and Jaramillo Aguado, Jesús Ángel (2001) Extension of bilinear forms on Banach spaces. Proceedings of the American Mathematical Society, 129 (12). pp. 3647-3656. ISSN 0002-9939

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Official URL: http://www.ams.org/journals/proc/2001-129-12/S0002-9939-01-05986-X/S0002-9939-01-05986-X.pdf


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Abstract

We study the extension of bilinear and multilinear forms from a given subspace of a Banach space to the whole space. Precisely, an isomorphic embedding j : E --> X is said to be (linearly) N-exact if N-linear forms on E can be (linear and continuously) extended to X through j. We present some necessary and sufficient conditions for j to be 2-exact, as well as several examples of 2-exact embeddings. We answer a problem of Zalduendo: in a cotype 2 space bilinear extendable and integral forms coincide.


Item Type:Article
Uncontrolled Keywords:Bilinear forms; tensor product; cotype-2 space; embedding
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16650
Deposited On:09 Oct 2012 10:18
Last Modified:09 Aug 2018 10:04

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