MAPPINGS BETWEEN BANACH SPACES

Abstract

Let X be a Banach space and let X be a class of spaces isomorphic to X with a pseudo metric delta(Y,Z) = inf{ln|T| |T^-1|:  Y,Z in X, T:Y->Z is an isomorphism}. We make use of linear functionals in dual space X to obtain bounds for delta(X, H), where H denotes a Hilbert space, so that X is a uniformly nonsquare space or X is a space with uniform normal structure
respectively.