Nonlinear *-Lie Higher Derivations of Standard Operator Algebras

Mohammad Ashraf 1 , Shakir Ali 2  and Bilal Ahmad Wani 1
  • 1 Department of Mathematics, Aligarh Muslim University,, Aligarh, India
  • 2 Department of Mathematics, Aligarh Muslim University,, Aligarh, India

Abstract

Let ℌ be an in finite-dimensional complex Hilbert space and A be a standard operator algebra on ℌ which is closed under the adjoint operation. It is shown that every nonlinear *-Lie higher derivation D = {δn}gn∈N of A is automatically an additive higher derivation on A. Moreover, D = {δn}gn∈N is an inner *-higher derivation.

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