Operator radii and unitary operators

Abstract

Let ρ 1 and wρ(A) be the operator radius of a linear operator A . Suppose m is a positive integer. It is shown that for a given invertible linear operator A acting on a Hilbert space, one has wρ (A−m) wρ (A)−m . The equality holds if and only if A is a multiple of a unitary operator. Mathematics subject classification (2010): 47A20, 47A12, 15A60.