Numerical Radii for Tensor Products of Operators

Hwa Long Gau, Kuo Zhong Wang, Pei Yuan Wu

研究成果: 雜誌貢獻期刊論文同行評審

4 引文 斯高帕斯(Scopus)

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 A ⊗ B are related by the inequalities (Formula presented.). In this paper, we show that (1) if (Formula presented.), then w(A) = ρ(A) or w(B) = ρ(B), where ρ(·) denotes the spectral radius of an operator, and (2) if A is hyponormal, then (Formula presented.). 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-Foiaş dilation theory.

原文???core.languages.en_GB???
頁(從 - 到)375-382
頁數8
期刊Integral Equations and Operator Theory
78
發行號3
DOIs
出版狀態已出版 - 3月 2014

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