標題: Numerical ranges of nilpotent operators
作者: Gau, Hwa-Long
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: numerical range;numerical radius;nilpotent operator
公開日期: 1-Aug-2008
摘要: For any operator A on a Hilbert space, let W(A), w(A) and w(0)(A) denote its numerical range, numerical radius and the distance from the origin to the boundary of its numerical range, respectively. We prove that if A(n) = 0, then w(A) <= (n - 1)w(0)(A), and, moreover, if A attains its numerical radius, then the following are equivalent: (1) w(A) = (n - 1)w(0)(A), (2)A is unitarily equivalent to an operator of the form aA(n) circle plus A', where a is a scalar satisfying vertical bar a vertical bar = 2w(0)(A), A(n) is the n-by-n matrix [GRAPHICS] and A' is some other operator, and (3) W(A) = bW(A(n)) for some scalar b. (C) 2008 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.laa.2008.03.029
http://hdl.handle.net/11536/8506
ISSN: 0024-3795
DOI: 10.1016/j.laa.2008.03.029
期刊: LINEAR ALGEBRA AND ITS APPLICATIONS
Volume: 429
Issue: 4
起始頁: 716
結束頁: 726
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