Korean J. Math. Vol. 31 No. 3 (2023) pp.313-321
DOI: https://doi.org/10.11568/kjm.2023.31.3.313

Non-linear product LM∗−ML∗ on prime ∗−algebras

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Published: Sep 30, 2023
Keywords:
Prime *-algebra, additive map., non-linear product
Mathematics Subject Classification:
46J10, 47B48, 46L10

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Mohd Arif Raza
Department of Mathematics, College of Science & Arts-Rabigh, King Abdulaziz University, Jeddah, Saudi Arabia.
Tahani Al-Sobhi
Department of Mathematics, College of Science & Arts-Rabigh, King Abdulaziz University, Jeddah, Saudi Arabia.

Abstract

In this paper, we explore the additivity of the map Ω:A→A that satisfies Ω([L,M]∗)=[Ω(M),L]∗+[M,Ω(L)]∗,
where [L,M]∗=LM∗−ML∗, for all L,M∈A, a prime ∗−algebra with unit I. Additionally we show that if Ω(αI) is self-adjoint operator for α∈{1,i}, then Ω=0.



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