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
