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Extension of bilinear forms on Banach spaces

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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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
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