Mediterranean Journal of Mathematics

, Volume 13, Issue 3, pp 1167–1175 | Cite as

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



Let \({\mathfrak{M}}\) be a Hilbert C*-module on a C*-algebra \({\mathfrak{A}}\) and let \({End_\mathfrak{A}(\mathfrak{M})}\) be the algebra of all operators on \({\mathfrak{M}}\). In this paper, first the continuity of \({\mathfrak{A}}\)-module homomorphism derivations on \({End_\mathfrak{A}(\mathfrak{M})}\) is investigated. We give some sufficient conditions on which every derivation on \({End_\mathfrak{A}(\mathfrak{M})}\) is inner. Next, we study approximately innerness of derivations on \({End_\mathfrak{A}(\mathfrak{M})}\) for a σ-unital C*-algebra \({\mathfrak{A}}\) and full Hilbert \({\mathfrak{A}}\)-module \({\mathfrak{M}}\). Finally, we show that every bounded linear mapping on \({End_\mathfrak{A}(\mathfrak{M})}\) which behave like a derivation when acting on pairs of elements with unit product, is a Jordan derivation.

Mathematics Subject Classification

Primary 47B47 Secondary 47B49 


Hilbert C*-modules derivations inner derivations 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Mostafa Kafi Moghadam
    • 1
  • M. Miri
    • 1
  • A. R. Janfada
    • 1
  1. 1.Department of MathematicsBirjand University, BirjandBirjandIran

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