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Title: Unitary similarity invariant function preservers of skew products of operators
Authors: Cui, JL
Li, CK
Sze, NS 
Keywords: Unitary similarity invariant function
Generalized numerical radius
Pseudo spectrum
Issue Date: 2017
Publisher: Academic Press
Source: Journal of mathematical analysis and applications, 2017, v. 454, no. 2, p. 716-729 How to cite?
Journal: Journal of mathematical analysis and applications 
Abstract: Let B(H) denote the Banach algebra of all bounded linear operators on a complex Hilbert space H with dim H >= 3, and let A and B be subsets of B(H) which contain all rank one operators. Suppose F(.) is a unitary invariant norm, the pseudo spectra, the pseudo spectral radius, the C-numerical range, or the C-numerical radius for some finite rank operator C. The structure is determined for surjective maps.1, : A B satisfying F(A*B) = F(Phi(A)*Phi(B)) for all A, B is an element of A. To establish the proofs, some general results are obtained for functions F:F-1(H) boolean OR {0}-> [0,+infinity), where F-1(H) is the set of rank one operators in B(H), satisfying (a) F(mu UAU*) = F(A) for a complex unit mu, A is an element of F-1(H) and unitary U is an element of B(H), (b) for any rank one operator X is an element of F-1(H) the map t -> F(tX) on [0, infinity) is strictly increasing, and (c) the set {F(X) : X E.F-1 (H) and parallel to X parallel to = 1} attains its maximum and minimum.
ISSN: 0022-247X
EISSN: 1096-0813
DOI: 10.1016/j.jmaa.2017.04.072
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