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Castillo, Jesús M.F. García, R. Jaramillo Aguado, Jesús Ángel 2023-06-20T16:59:26Z 2023-06-20T16:59:26Z 2001 0002-9939 http://dox.doi.org/10.1090/S0002-9939-01-05986-X https://hdl.handle.net/20.500.14352/57581 http://www.ams.org/journals/proc/2001-129-12/S0002-9939-01-05986-X/S0002-9939-01-05986-X.pdf http://www.ams.org/ 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. eng restricted access Extension of bilinear forms on Banach spaces journal article