Rocky Mountain Journal of Mathematics

Non-linear $\lambda $-Jordan triple $\ast $-derivation on prime $\ast $-algebras

A. Taghavi, M. Nouri, M. Razeghi, and V. Darvish

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Abstract

Let $\mathcal {A}$ be a prime $\ast $-algebra and $\Phi $ a $\lambda $-Jordan triple derivation on $A$, that is, for every $A,B,C \in \mathcal {A}$, $$\Phi (A\diamond _{\lambda } B \diamond _{\lambda }C)=\Phi (A)\diamond _{\lambda }B\diamond _{\lambda } C+A\diamond _{\lambda }\Phi (B)\diamond _{\lambda }C+A\diamond _{\lambda } B\diamond _{\lambda }\Phi (C),$$ where $A\diamond _{\lambda } B = AB + \lambda BA^{\ast }$ such that a complex scalar $|\lambda |\neq 0,1$, and $\Phi $ is additive. Moreover, if $\Phi (I)$ is self-adjoint, then $\Phi $ is a $\ast $-derivation.

Article information

Source
Rocky Mountain J. Math., Volume 48, Number 8 (2018), 2705-2716.

Dates
First available in Project Euclid: 30 December 2018

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1546138828

Digital Object Identifier
doi:10.1216/RMJ-2018-48-8-2705

Mathematical Reviews number (MathSciNet)
MR3895000

Zentralblatt MATH identifier
06999281

Subjects
Primary: 47B48: Operators on Banach algebras 46J10: Banach algebras of continuous functions, function algebras [See also 46E25] 46L10: General theory of von Neumann algebras

Keywords
Jordan triple derivation prime $\ast $-algebra additive map

Citation

Taghavi, A.; Nouri, M.; Razeghi, M.; Darvish, V. Non-linear $\lambda $-Jordan triple $\ast $-derivation on prime $\ast $-algebras. Rocky Mountain J. Math. 48 (2018), no. 8, 2705--2716. doi:10.1216/RMJ-2018-48-8-2705. https://projecteuclid.org/euclid.rmjm/1546138828


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