Bi-Skew Lie (Jordan) Product on Factor Von Neumann Algebras

Authors

  • Mohd Arif Raza Department of Mathematics, College of Science & Arts-Rabigh, King Abdulaziz University, Jeddah, Saudi Arabia https://orcid.org/0000-0001-6799-8969 (unauthenticated)
  • Huda Eid Almehmadi Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia

DOI:

https://doi.org/10.37256/cm.5420245028

Keywords:

von Neumann algebra, bi-skew Lie (Jordan) product, ∗-isomorphism

Abstract

In this manuscript, we characterize the bijective mapping mceclip0-951a75e35b20050b03d0ad0e11dff664.png between two von Neumann algebras mceclip1-087ffb4e3ec663023ea002f75a2377ba.png and mceclip2-c1babbbd6f3f979a338e33f414492253.png with dim ⩾ 1. The mapping Λ is to satisfy the following condition on the mixed bi-skew Lie (Jordan) product mceclip3-1dafc3d026ed6c610ce5d355f8306712.png, for all mceclip4-560bb6bf477fd6318e16c6ca234164fe.png, where the bi-skew Lie (Jordan) product is defined as mceclip5-1600657682a30a0bcf0e3f4014aa303c.png , and mceclip6.png . Specifically, we elaborate on the properties of the mapping Λ, establishing that it is additive, a∗-somorphism, and linear.

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Published

2024-12-25

Issue

Contemporary Mathematics, Volume 5 Issue 4 (2024), 4132-6581

Section

Research Article

License

Copyright (c) 2024 Mohd Arif Raza, et al.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

1.
Bi-Skew Lie (Jordan) Product on Factor Von Neumann Algebras. Contemp. Math. [Internet]. 2024 Dec. 25 [cited 2025 Dec. 24];5(4):6495-514. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/5028