A class of unitarily invariant norms on B(H)

Let H be a complex Hilbert space and let B(H) be the algebra of all bounded linear operators on H. For c = (c(1),...,c(k)), where c(1) greater than or equal to ... greater than or equal to c(k) > 0 and p greater than or equal to 1, define the (c, p)-norm of A is an element of B(H) by [GRAPHICS] 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).