Banach ideals of operators with applications to the finite dimensional structure of Banach spaces

Abstract

We present a few applications of the theory of Banach ideals of operators. In particular, we give operator characterizations of the ℒp spaces, compute the relative projection constant of isometric embeddings of Hilbert spaces inLp-spaces, and show that Π1 (E, F), the space of absolutely summing operators, is reflexive ifE andF are reflexive andE has the approximation property.