標題: Equality of three numerical radius inequalities
作者: Gau, Hwa-Long
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: Numerical range;Numerical radius;Operator norm;Generalized Aluthge transform
公開日期: 1-十月-2018
摘要: For an n-by-n matrix A, let w(A) and parallel to A parallel to denote its numerical radius and operator norm, respectively. The following three inequalities, each a strengthening of w(A) <= parallel to A parallel to, are known to hold: w(A)(2) <= (parallel to A parallel to(2) + w(A(2)))/2, w(A) <= (parallel to A parallel to + parallel to A(2)parallel to(1/2))/2, and w(A) <= (parallel to A parallel to + w(Delta(t)(A)))/2 (0 <= t <= 1), where Delta(t)(A) is the generalized Aluthge transform of A. In this paper, we derive necessary and sufficient conditions in terms of the operator structure of A for which the inequalities become equalities. (C) 2018 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.laa.2018.05.021
http://hdl.handle.net/11536/148010
ISSN: 0024-3795
DOI: 10.1016/j.laa.2018.05.021
期刊: LINEAR ALGEBRA AND ITS APPLICATIONS
Volume: 554
起始頁: 51
結束頁: 67
顯示於類別:期刊論文