Geometric Interpolation in Symmetrically-normed Ideals

Abstract

The aim of this work is to apply the complex interpolation method to norms of n-tuples of operators in a symmetrically-normed ideal J contained in B(H) defined by a symmetric norming function (s.n.f.). The norms considered define Finsler metrics in a certain manifold of positive operators, and can be regarded as weighted norms, the weight being a positive invertible operator.