Banach ideals of operators with applications

Abstract

We present some results concerning the general theory of Banach ideals of operators and give several applications to Banach space theory. We give, in Section 3, new proofs of several recent results, as well as new operator characterizations of the L p -spaces of Lindenstrauss and Pelczynski. In Section 4 we prove that the space of absolutely summing operators from E to F is reflexive if both E and F are reflexive and E has the approximation property. Section 5 concerns Hilbert spaces. In particular, we compute the relative projection constant of Hilbert spaces in L p (μ)-spaces.