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- W1574271653 abstract "Suppose that $frak A$ is a $C^*$-algebra acting on a Hilbert space $frak K$, and $varphi, psi$ are mappings from $frak A$ into $B(frak K)$ which are not assumed to be necessarily linear or continuous. A $(varphi, psi)$-derivation is a linear mapping $d: frak A to B(frak K)$ such that $$d(ab)=varphi(a)d(b)+d(a)psi(b)quad (a,bin frak A).$$ We prove that if $varphi$ is a multiplicative (not necessarily linear) $*$-mapping, then every $*$-$(varphi,varphi)$-derivation is automatically continuous. Using this fact, we show that every $*$-$(varphi,psi)$-derivation $d$ from $frak A$ into $B(frak K)$ is continuous if and only if the $*$-mappings $varphi$ and $psi$ are left and right $d$-continuous, respectively." @default.
- W1574271653 created "2016-06-24" @default.
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- W1574271653 date "2007-11-01" @default.
- W1574271653 modified "2023-09-26" @default.
- W1574271653 title "Achievement of continuity of $(varphi,psi)$-derivations without linearity" @default.
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- W1574271653 doi "https://doi.org/10.36045/bbms/1195157133" @default.
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