Extended form of $ (\zeta, \eta) $-derivation of von Neumann algebra

Abu Zaid Ansari; Faiza Shujat; Ahlam Fallatah; Abu Zaid Ansari; Faiza Shujat; Ahlam Fallatah

doi:10.3934/math.2026345

AIMS Mathematics

2026, Volume 11, Issue 3: 8407-8416. doi: 10.3934/math.2026345

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Extended form of $ (\zeta, \eta) $-derivation of von Neumann algebra

1.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Saudi Arabia
2.
Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia

Received: 05 February 2026 Revised: 17 March 2026 Accepted: 24 March 2026 Published: 30 March 2026
MSC : 16N60, 16W25, 46L10, 47L40

Let $ \mathcal{U} $ be regarded as a CSL subalgebra of a von Neumann algebra operating on a Hilbert space $ \mathcal{H} $. Let $ \mathcal{G}_\mathbf{h}, \mathbf{h}: \mathcal{U}\to \mathcal{U} $ denote two significant linear mappings that intricately fulfill certain essential algebraic identities. As a result, $ \mathcal{G}_\mathbf{h} $ emerges as a generalized $ (\zeta, \eta) $-derivation, preserving a fundamental relationship with the associated $ (\zeta, \eta) $-derivation $ \mathbf{h} $ functioning within the framework of $ \mathcal{U} $.
- semiprime rings,
- algebra,
- automorphisms,
- generalized $ (\zeta, \eta) $-derivation
Citation: Abu Zaid Ansari, Faiza Shujat, Ahlam Fallatah. Extended form of $ (\zeta, \eta) $-derivation of von Neumann algebra[J]. AIMS Mathematics, 2026, 11(3): 8407-8416. doi: 10.3934/math.2026345

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Abstract

Let $ \mathcal{U} $ be regarded as a CSL subalgebra of a von Neumann algebra operating on a Hilbert space $ \mathcal{H} $. Let $ \mathcal{G}_\mathbf{h}, \mathbf{h}: \mathcal{U}\to \mathcal{U} $ denote two significant linear mappings that intricately fulfill certain essential algebraic identities. As a result, $ \mathcal{G}_\mathbf{h} $ emerges as a generalized $ (\zeta, \eta) $-derivation, preserving a fundamental relationship with the associated $ (\zeta, \eta) $-derivation $ \mathbf{h} $ functioning within the framework of $ \mathcal{U} $.

References

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