A class of unitarily invariant norms on B(H)

Let H be a complex Hubert space and let B(H) be the algebra of all bounded linear operators on H. For c = (c1, ..., ck), where c1 ≥ ⋯ ≥ Ck > 0 and p ≥ 1, define the (c,p)-norm of A ∈ B(H) by ∥A∥c,p = (∑i=1 kcisi(A)p) 1/p where si(A) denotes the ith s-numbers of A. In this paper we study some basic properties of this norm and give a characterization of the extreme points of its closed unit ball. Using these results, we obtain a description of the corresponding isometric isomorphisms on B(H). ©2000 American Mathematical Society.published_or_final_versio