Geometric interpolation in symmetrically-normed ideals

The aim of this work is to apply the complex interpolation method to norms of n-tuples of operators in a symmetrically-normed ideal Jϕ⊆B(H) defined by a ϕ 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 ϕ-norms, the weight being a positive invertible operator.