Isomorphic Embeddings and Harmonic Behaviour of Smooth Operators

Abstract

Let Y be a Banach space, 1<p<infinity. We give a simple criterion for embedding l_p into Y, namely it suffices that the positive cone l_p+ embeds into Y.

This result is applied to the study of highly smooth operators from l_p into Y (p is not an even integer). The main result is that every such operator has a harmonic behaviour unless l_(p/K) embeds into Y for some integer K.