Local operators and derivations on 𝐶*-algebras

Batty, C. J. K.

doi:10.1090/S0002-9947-1985-0766223-3

Local operators and derivations on $C^ \ast$-algebras
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Trans. Amer. Math. Soc. 287 (1985), 343-352 Request permission

Abstract:

The variations on a theme of locality for a pair of operators $(H,K)$ on a ${C^\ast }$-algebra $\mathfrak {A}$ are expressed algebraically. If $K$ is a $\ast$-derivation generating an action of $\mathbb {R}$ on $\mathfrak {A}$, and $H$ is $\ast$-linear and $K$-local, then, under certain restrictions, $H$ is shown to be very closely related to $K$.

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