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Local derivations of reflexive algebras
Authors:Jing Wu
Institution:Department of Mathematics, Qufu Normal University, Qufu, Shandong, 273165, People's Republic of China
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.

Keywords:Reflexive algebra  derivation  local derivation
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