Lie higher derivations on $B(X)$

Subject Areas : History and biography

S. Ebrahimi ¹

1 - Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran.

Received: 2015-07-13 Accepted : 2015-11-17 Published : 2015-08-01

Keywords: Lie derivation, Lie higher derivations, higher derivations,

Abstract :

Let $X$ be a Banach space of $\dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)\to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $\tau : B(X)\to FI$ vanishing at commutators $[A, B]$ for all $A, B\in B(X)$ such that $L = D + \tau$.

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