Certain isometries of rectangular complex matrices

Abstract

AbstractIf s1(A) ⩾ ⋯ ⩾ sm(A) are the singular values of A ϵ Mm,n(C), and if 1 ⩽k ⩽m ⩽ and p ⩾ 1, then φp,k(A) = (∑i=1ksip(A)1p is a unitarily invariant norm. In this paper a complete determination of the extreme points on the corresponding unit spheres is accomplished in all cases, enabling the isometries with respect to Φp,k to be determined in the case p = 1. This removes the restriction m = n in an earlier paper of the author and Marcus