Automatic continuity of -derivations on -algebras |
| |
Authors: | Madjid Mirzavaziri Mohammad Sal Moslehian |
| |
Affiliation: | Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran ; Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran |
| |
Abstract: | Let be a -algebra acting on a Hilbert space , let be a linear mapping and let be a -derivation. Generalizing the celebrated theorem of Sakai, we prove that if is a continuous -mapping, then is automatically continuous. In addition, we show the converse is true in the sense that if is a continuous --derivation, then there exists a continuous linear mapping such that is a --derivation. The continuity of the so-called - -derivations is also discussed. |
| |
Keywords: | $*$-$(sigma tau)$-derivation $sigma$-derivation derivation automatic continuity $C^*$-algebra |
|
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 |
|
点击此处可从《Proceedings of the American Mathematical Society》下载全文 |
|