Maximizing numerical radii of weighted shifts under weight permutations

Abstract

Let omega(i) is an element of C (1 <= i <= n) and I is an element of S-n, the symmetric group of all permutations of 1, 2,...,n. Suppose A(I) is the weighted cyclic matrix [GRAPHICS] and omega(A(I)) denotes its numerical radius. We characterize those zeta is an element of S-n which satisfy omega(A(zeta)) = max(vertical bar is an element of Sn) omega(A(I)). The characterizations for unilateral and bilateral weighted (backward) shifts are also obtained. Crown Copyright (C) 2012 Published by Elsevier Inc. All rights reserved.