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Research Article | Open Access

Nonlinear mixed type product [K,F]∗⊙D on ∗-algebras

Junaid Nisar1( ), Turki Alsuraiheed2( ), Nadeem ur Rehman3
Department of Applied Sciences, Symbiosis Institute of Technology, Symbiosis International (Deemed) University, Lavale, Pune, India
Department of Mathematics, College of Science, King Saud University P.O. Box 2455 Riyadh 11451, Saudi Arabia
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
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Abstract

Let A be a unital ∗-algebra containing a non-trivial projection. In this paper, we prove that if a map Ω : A → A such that

Ω([K,F]∗⊙D)=[Ω(K),F]∗⊙D+[K,Ω(F)]∗⊙D+[K,F]∗⊙Ω(D),

where [K,F]∗=KF−FK∗ and K⊙F=K∗F+FK∗ for all K,F,D∈A, then Ω is an additive ∗-derivation. Furthermore, we extend its results on factor von Neumann algebras, standard operator algebras and prime ∗-algebras. Additionally, we provide an example illustrating the existence of such maps.

Keywords

mixed bi-skew Jordan triple derivation∗-derivation∗- algebrainvolution
CLC number: 16W10, 46K15, 47B47

References

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AIMS Mathematics
Volume 9 Issue 8,
August 2024
Pages 21596-21608
DOI: 10.3934/math.20241049

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Cite this article:
Nisar J, Alsuraiheed T, Rehman Nu. Nonlinear mixed type product [K,F]∗⊙D on ∗-algebras. AIMS Mathematics, 2024, 9(8): 21596-21608. https://doi.org/10.3934/math.20241049

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Received: 14 May 2024
Revised: 19 June 2024
Accepted: 26 June 2024
Published: 15 August 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)