Extension of bilinear forms on Banach spaces

Castillo, Jesús; García, Ricardo; Jaramillo, Jesús

doi:10.1090/S0002-9939-01-05986-X

Extension of bilinear forms on Banach spaces
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by Jesús M. F. Castillo, Ricardo García and Jesús A. Jaramillo PDF

Proc. Amer. Math. Soc. 129 (2001), 3647-3656 Request permission

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 $j: E \to X$ 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.

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