Article

Multiplicative ∗-lie triple higher derivations of standard operator algebras

Published in: Quaestiones Mathematicae
Volume 42 , issue 7 , 2019 , pages: 857–884

DOI: 10.2989/16073606.2018.1502213

Author(s): Mohammad Ashraf Department of Mathematics, India , Bilal Ahmad Wani Department of Mathematics, India , Feng Wei School of Mathematics and Statistics, P.R. China

Keywords: 47B47 , 16W25 , 46K15 , 47B47 , 16W25 , 46K15

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Abstract

Let be a standard operator algebra on an infinite dimensional complex Hilbert space containing identity operator I. In this paper it is shown that if is closed under the adjoint operation, then every multiplicative ∗-Lie triple derivation is a linear ∗-derivation. Moreover, if there exists an operator S ∈

such that S + S^∗ = 0 then d(U) = U S − SU for all U ∈

, that is, d is inner. Furthermore, it is also shown that any multiplicative ∗-Lie triple higher derivation D = {δ_n}_n∈ℕ of is automatically a linear inner higher derivation on with d(U)^∗ = d(U^∗).

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