Local derivations of reflexive algebras

Wu, Jing

doi:10.1090/S0002-9939-97-03720-9

Local derivations of reflexive algebras
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by Jing Wu

Proc. Amer. Math. Soc. 125 (1997), 869-873

DOI: https://doi.org/10.1090/S0002-9939-97-03720-9

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Abstract:

Let $\mathcal A$ be a reflexive algebra in Banach space $X$ such that both $O_+\not =O$ and $X_-\not =X$ in $\operatorname {Lat} \mathcal A$, the invariant subspace lattice of $\mathcal A$, then every derivation of $\mathcal A$ into itself is spatial. Furthermore, if $X$ is additionally reflexive, then the set of all inner derivations of $\mathcal A$ into itself is topologically algebraically reflexive.

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