Extension of bilinear forms on Banach spaces

Abstract

Ve 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) AT-exact if JV-linear forms on E can be (linear and continuously) extended to A' 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. ©2001 American Mathematical Society.