Convexoid and generalized derivations |
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Authors: | M. Barraa |
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Affiliation: | Department of Mathematics, Faculty of Sciences, Semlalia, Marrakech, Morocco |
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Abstract: | Let E,F be two Banach spaces and let S be a symmetric norm ideal of L(E,F). For AL(F) and BL(E) the generalized derivation δS,A,B is the operator on S that sends X to AX−XB. A bounded linear operator is said to be convexoid if its (algebraic) numerical range coincides with the convex hull of its spectrum. We show that δS,A,B is convexoid if and only if A and B are convexoid. |
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Keywords: | Elementary operator Convexoid operator Numerical range spectrum Derivation |
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