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• W1722534106 abstract "Let $mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semi-finite trace $tau$ and let $S_0(tau)$ be the algebra of all $tau$-compact operators affiliated with $mathcal{M}$. Let $E(tau)subseteq S_0(tau)$ be a symmetric operator space (on $mathcal{M}$) and let $mathcal{E}$ be a symmetrically-normed Banach ideal of $tau$-compact operators in $mathcal{M}$. We study (i) derivations $delta$ on $mathcal{M}$ with the range in $E(tau)$ and (ii) derivations on the Banach algebra $mathcal{E}$. In the first case our main results assert that such derivations are continuous (with respect to the norm topologies) and also inner (under some mild assumptions on $E(tau)$). In the second case we show that any such derivation is necessarily inner when $mathcal{M}$ is a type $I$ factor. As an interesting application of our results for the case (i) we deduce that any derivation from $mathcal{M}$ into an $L_p$-space, $L_p(mathcal{M},tau)$, ($1<p<infty$) associated with $mathcal{M}$ is inner." @default.
• W1722534106 created "2016-06-24" @default.
• W1722534106 creator A5037022930 @default.
• W1722534106 creator A5079947779 @default.
• W1722534106 date "2012-04-18" @default.
• W1722534106 modified "2023-09-27" @default.
• W1722534106 title "Derivations in the Banach ideals of $τ$-compact operators" @default.
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