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We study the extension of bilinear forms from a given subspace of an L1 -space to the whole space. Precisely, an isomorphic embedding j: E → X is said to be (linearly) 2-exact if bilinear forms on E can be (linear and continuously) extended to X through j . We present some necesary and some sufficient conditions for an embedding j: E → X to be 2-exact when X is an L1 -space., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

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., DGICYT, Depto. de Análisis Matemático y Matemática Aplicada, Fac. de Ciencias Matemáticas, TRUE, pub

[EN] This paper contains a study of the structure of the Frechet space L-p- , 1 < P less than or equal to infinity, defined as the intersection of Lq[0, 1] for q < p, and endowed with the projective topology. The main topics covered are: normable, Schwartz and nuclear subspaces of L-p-;construction of uncomplemented copies of l(2) inside L-p- for p < 2; construction of Montel non-Schwartz subspaces; the space L-p- is primary.