Continuity of derivations of algebras of locally measurable operators |
| |
Authors: | A F Ber V I Chilin F A Sukochev |
| |
Institution: | 1. Department of Mathematics, National University of Uzbekistan, Vuzgorodok, 100174, Tashkent, Uzbekistan 2. School of Mathematics and Statistics, University of New South Wales, Sydney, NSW, 2052, Australia
|
| |
Abstract: | 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 ${\delta:{\mathcal{M}}\rightarrow LS({\mathcal{M}})}$ 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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|