Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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CONTINUITY OF (α,β)-DERIVATIO OF OPERATOR ALGEBRAS

  • Hou, Chengjun (Institute of Operations Research Qufu Normal University) ;
  • Meng, Qing (School of Mathematical Sciences Qufu Normal University)
  • Received : 2010.04.15
  • Published : 2011.07.01
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Abstract

We investigate the continuity of (${\alpha},{\beta}$)-derivations on B(X) or $C^*$-algebras. We give some sufficient conditions on which (${\alpha},{\beta}$)-derivations on B(X) are continuous and show that each (${\alpha},{\beta}$)-derivation from a unital $C^*$-algebra into its a Banach module is continuous when and ${\alpha}$ ${\beta}$ are continuous at zero. As an application, we also study the ultraweak continuity of (${\alpha},{\beta}$)-derivations on von Neumann algebras.

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References

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  2. Characterization of some derivations on von Neumann algebras via left centralizers 2017, https://doi.org/10.1007/s11565-017-0290-2
  3. Continuity and Structure of Generalized $$\varvec{(\phi ,\psi )}$$ ( ϕ , ψ ) -Derivations 2017, https://doi.org/10.1007/s00025-017-0731-3