A Note on Derivations on the Algebra of Operators in Hilbert C-Modules

Let M be a Hilbert C *-module on a C *-algebra A and let E n d A ( M ) be the algebra of all operators on M . In this paper, first the continuity of A -module homomorphism derivations on E n d A ( M ) is investigated. We give some sufficient conditions on which every derivation on E n d A ( M ) is i...

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Bibliographic Details
Published in:Mediterranean journal of mathematics 2016-06, Vol.13 (3), p.1167-1175
Main Authors: Kafi Moghadam, Mostafa, Miri, M., Janfada, A. R.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let M be a Hilbert C *-module on a C *-algebra A and let E n d A ( M ) be the algebra of all operators on M . In this paper, first the continuity of A -module homomorphism derivations on E n d A ( M ) is investigated. We give some sufficient conditions on which every derivation on E n d A ( M ) is inner. Next, we study approximately innerness of derivations on E n d A ( M ) for a σ -unital C *-algebra A and full Hilbert A -module M . Finally, we show that every bounded linear mapping on E n d A ( M ) which behave like a derivation when acting on pairs of elements with unit product, is a Jordan derivation.
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-015-0538-y