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

Seddik, Ameur

Linear Algebra Appl. 338, No. 1-3, 239-244 (2001).

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 \(W_0(A)-W_0(B)\).

Reviewer: Aleksej Turnšek (Ljubljana)

MSC:

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

Keywords:

Hilbert space; bounded linear operator; generalised derivation; elementary operator; numerical range

Citations:

Zbl 1016.47004

References:

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