Automatic continuity of  -derivations on  -algebras |
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| Authors: | Madjid Mirzavaziri Mohammad Sal Moslehian |
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| Institution: | Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran ; Department of Mathematics, Ferdowsi University, P.O. Box 1159, Mashhad 91775, Iran |
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| 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. |
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| Keywords: | $*$-$(\sigma \tau)$-derivation $\sigma$-derivation derivation automatic continuity $C^*$-algebra |
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