The numerical range of elementary operators. II. (English) Zbl 1032.47020

This article is a continuation of A. Seddik [Integral Equations Oper. Theory 43, 248-252 (2002; Zbl 1016.47004)]. For two Hilbert space operators \(A\) and \(B\), the author proves that: (i) the generalized derivation \(\delta_{A,B}\) is convexoid if and only if \(A\) and \(B\) are convexoid; (ii) the operators \(\delta_{A,B}\) and \(\delta_{A,B}|\mathcal{C}_p\) have the same numerical range \(W_0(A)-W_0(B)\).


47B47 Commutators, derivations, elementary operators, etc.
47A12 Numerical range, numerical radius
47B10 Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.)
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory


Zbl 1016.47004
Full Text: DOI


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