標題: Numerical Radii for Tensor Products of Operators
作者: Gau, Hwa-Long
Wang, Kuo-Zhong
Wu, Pei Yuan
應用數學系
Department of Applied Mathematics
關鍵字: Numerical range;numerical radius;tensor product;hyponormal operator
公開日期: 1-三月-2014
摘要: For bounded linear operators A and B on Hilbert spaces H and K, respectively, it is known that the numerical radii of A, B and are related by the inequalities . In this paper, we show that (1) if , then w(A) = rho(A) or w(B) = rho(B), where rho(center dot) denotes the spectral radius of an operator, and (2) if A is hyponormal, then . Here (2) confirms a conjecture of Shiu's and is proven via dilating the hyponormal A to a normal operator N with the spectrum of N contained in that of A. The latter is obtained from the Sz.-Nagy-FoiaAY dilation theory.
URI: http://dx.doi.org/10.1007/s00020-013-2098-5
http://hdl.handle.net/11536/24013
ISSN: 0378-620X
DOI: 10.1007/s00020-013-2098-5
期刊: INTEGRAL EQUATIONS AND OPERATOR THEORY
Volume: 78
Issue: 3
起始頁: 375
結束頁: 382
顯示於類別:期刊論文


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  1. 000332581500003.pdf