Extension of (η,φ)-Derivation on the CSL Subalgebra of von Neumann Algebra

Authors

  • Abu Zaid Ansari Department of Mathematics, Faculty of Science, Islamic University of Madinah, K.S.A.
  • Faiza Shujat Department of Mathematics, College of Science, Taibah University, Madinah, K.S.A. https://orcid.org/0000-0001-5537-9837 (unauthenticated)
  • Ahlam Fallatah Department of Mathematics, College of Science, Taibah University, Madinah, K.S.A.

DOI:

https://doi.org/10.37256/cm.7120267337

Keywords:

von Neumann algebra, semiprime rings, generalized (<i>η</i>, <i>φ</i>)-derivation and linear mappings

Abstract

This article aims to demonstrate the following: consider mceclip0-a561d420f14e3da18ef07ff7a163d4c4.png, a Commutative Subspace Lattice (CSL) subalgebra of a von Neumann algebra acting on a Hilbert space mceclip1-f0538b865d407d52f65f63697ae5da66.png. Suppose that mceclip2-ec019aa646420e14e4bcd0dd1566951d.pngare two linear mappings that satisfy some certain functional identities. Then mceclip3-73fca5b7ce95c2ea22a55ebc9752071c.pngis a generalized (η, φ)-derivation with associated (η, φ)-derivation mceclip4-ea9fa0a448e3a6ded8c0a7cf0ac8647e.png in mceclip0-a561d420f14e3da18ef07ff7a163d4c4.png, where η and φ are automorphisms in mceclip0-a561d420f14e3da18ef07ff7a163d4c4.png.

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Published

2025-11-24

Issue

Contemporary Mathematics, Volume 7 Issue 1 (2026), Forthcoming...

Section

Research Article

License

Copyright (c) 2025 Faiza Shujat, et al.

Creative Commons License

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

How to Cite

1.
Extension of (η,φ)-Derivation on the CSL Subalgebra of von Neumann Algebra. Contemp. Math. [Internet]. 2025 Nov. 24 [cited 2025 Dec. 24];7(1):1-11. Available from: https://ojs353.mebyme.cn/index.php/CM/article/view/7337