Operator radii and unitary operators
Tsuyoshi Andô, Chi-Kwong Li · Operators and Matrices · 2010
Let 1 and w (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 w (A -m ) w (A) -m . The equality holds if and only if A is a multiple of a unitary operator.