標題: Matrix powers with circular numerical range 作者: Gau, Hwa-LongWang, Kuo-Zhong應用數學系Department of Applied Mathematics 關鍵字: Numerical range;Numerical radius;Numerical contraction 公開日期: 1-Oct-2020 摘要: Let K-2 = [GRAPHICS}, K-n be the n x n weighted shift matrix with weights root 2, [GRAPHICS}, root 2 for all n >= 3, and K-infinity be the weighted shift operator with weights root 2, 1, 1, 1, .... In this paper, we show that if an n x n nonzero matrix A satisfies W(A(k)) = W(A) for all 1 <= k <= n, then W(A) cannot be a (nondegenerate) circular disc. Moreover, we also show that W(A) = W(A(n-1)) = {z is an element of C : vertical bar z vertical bar <= 1} if and only if A is unitarily similar to K-n. Finally, we prove that if T is a numerical contraction on an infinite-dimensional Hilbert space H, then lim(n ->infinity) parallel to T(n)x parallel to = root 2 for some unit vector x is an element of H if and only if T is unitarily similar to an operator of the form K-infinity circle plus T' with w(T') <= 1. (C) 2020 Elsevier Inc. All rights reserved. URI: http://dx.doi.org/10.1016/j.laa.2020.05.039http://hdl.handle.net/11536/155089 ISSN: 0024-3795 DOI: 10.1016/j.laa.2020.05.039 期刊: LINEAR ALGEBRA AND ITS APPLICATIONS Volume: 603 起始頁: 190 結束頁: 211 Appears in Collections: Articles