Numerical radius inequalities for tensor product of operators

DOI10.1007/S12044-022-00722-2arXiv2203.12162MaRDI QIDQ6394452

Pintu Bhunia, Kallol Paul, Anirban Sen

Publication date: 22 March 2022

Abstract: The two well-known numerical radius inequalities for the tensor product $AotimesB$ acting on $mathbbHotimesmathbbK$, where $A$ and $B$ are bounded linear operators defined on complex Hilbert spaces $mathbbH$ and $mathbbK,$ respectively are, $frac12|A||B|leqw(AotimesB)leq|A||B|$ and $w(A)w(B)leqw(AotimesB)leqminw(A)|B|,w(B)|A|.$ In this article we develop new lower and upper bounds for the numerical radius $w(AotimesB)$ of the tensor product $AotimesB$ and study the equality conditions for those bounds.

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Numerical range, numerical radius (47A12) Equations and inequalities involving linear operators, with vector unknowns (47A50)

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