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Properties and preservers of numerical radius on skew Lie products of operators
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NSTL
Elsevier
Let H be a complex separable Hilbert space with dim H >= 3 and B(H) the Banach algebra of all bounded linear operators on H. Denote by w(A) the numerical radius of a bounded linear operator A is an element of B(H) and AB - BA* the skew Lie product of two operators A, B is an element of B(H). In this paper, it is shown that, if a surjective map Phi : B(H) -> B(H) satisfies w(AB-BA*) = w(Phi(A)Phi(B) - Phi(B)Phi(A)*) for all A, B is an element of B(H), then there exist a unitary operator U is an element of B(H), a functional h : B(H) -> {-1, 1} and a subset S subset of B(H) consisting of some normal operators such that Phi(A) = h(A)U AU* if A is an element of Phi(H) \ S and (I)(A) = Phi(A)U A*U* if A is an element of S. Particularly, if dim H < infinity, a complete characterization of S can be obtained. (C) 2021 Elsevier Inc. All rights reserved.
Numerical radiusSkew Lie productsBounded linear operatorsGeneral preserversFUNCTIONAL VALUESPOLYNOMIAL XYMAPSSUBSPACEMAPPINGSMATRICESRANGENORMS
NSTL
Elsevier
