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Rakočević’s property for generalized derivations

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Abstract

Given Banach spaces \(\mathcal {X}\) and \(\mathcal {Y}\) and Banach space operators \(A\in L(\mathcal {X})\) and \(B\in L(\mathcal {Y}).\) The generalized derivation \(\delta \in L(L(\mathcal {Y},\mathcal {X}))\) is defined by \(\delta (X)=AX-XB.\) In this article necessary and sufficient conditions ensuring that Rakočević’s property (w), on the one hand and its generalization (gw), on the other hand transfer from \(A\) and \(B\) to \(\delta \).

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Acknowledgments

The authors wish to express their indebtedness to the referee, for his suggestions and valuable comments on this paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences, University Chouaib Doukkali, 24000, El Jadida, El Jadida, Morocco

    Mohamed Amouch

  2. Department of Mathematics, Faculty of Science, University of Batna, 05000, Batna, Algeria

    Farida Lombarkia

Authors
  1. Mohamed Amouch
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  2. Farida Lombarkia
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Correspondence to Mohamed Amouch.

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Amouch, M., Lombarkia, F. Rakočević’s property for generalized derivations. Rend. Circ. Mat. Palermo 64, 57–66 (2015). https://doi.org/10.1007/s12215-014-0178-2

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  • DOI: https://doi.org/10.1007/s12215-014-0178-2

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