Continuity of derivations in algebras of locally measurable operators

Autor:	Ber, A. F., Chilin, V. I., Sukochev, F. A.
Rok vydání:	2011
Předmět:	Mathematics - Operator Algebras
Druh dokumentu:	Working Paper
Popis:	We prove that any derivation of the *-algebra $LS(\mathcal{M})$ of all locally measurable operators affiliated with a properly infinite von Neumann algebra $\mathcal{M}$ is continuous with respect to the local measure topology $t(\mathcal{M})$. Building an extension of a derivation $\delta:\mathcal{M}\longrightarrow LS(\mathcal{M})$ up to a derivation from $LS(\mathcal{M})$ into $LS(\mathcal{M})$, it is further established that any derivation from $\mathcal{M}$ into $LS(\mathcal{M})$ is $t(\mathcal{M})$-continuous. Comment: 31 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1108.5427 Zobrazit plný text záznamu View this record from Arxiv