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Jordan Derivations of Reflexive Algebras

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Abstract

Let \({\mathcal L}\) be a subspace lattice on a Banach space X and suppose that \({\vee\{L\in\mathcal L: L_- < X\}=X}\) or \({\land\{L_- : L \in \mathcal L, L>(0)\}=(0)}\) . Then each Jordan derivation from Alg\({\mathcal L}\) into B(X) is a derivation. This result can apply to completely distributive subspace lattice algebras, \({\mathcal J}\) -subspace lattice algebras and reflexive algebras with the non-trivial largest or smallest invariant subspace.

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Authors and Affiliations

  1. Department of Mathematics, Suzhou University, Suzhou, 215006, People’s Republic of China

    Fangyan Lu

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  1. Fangyan Lu
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Correspondence to Fangyan Lu.

Additional information

The research was supported by NNSFC (No. 10771154).

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Lu, F. Jordan Derivations of Reflexive Algebras. Integr. Equ. Oper. Theory 67, 51–56 (2010). https://doi.org/10.1007/s00020-010-1769-8

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  • DOI: https://doi.org/10.1007/s00020-010-1769-8

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