# CONTINUITY OF (α,β)-DERIVATIO OF OPERATOR ALGEBRAS

• Hou, Chengjun ;
• Meng, Qing
• Published : 2011.07.01
• 35 14

#### 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.

#### Keywords

automatic continuity;(${\alpha},{\beta}$)-derivation;Banach algebra;algebra;C*-algebra

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#### Cited by

1. Jordan (α,β)-Derivations on Operator Algebras vol.2017, 2017, https://doi.org/10.1155/2017/4757039
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