Linear maps on von Neumann algebras acting as Lie type derivation via local actions

Mohd Arif Raza; Aisha Jabeen; Abdul Nadim Khan; Husain Alhazmi; Mohd Arif Raza; Aisha Jabeen; Abdul Nadim Khan; Husain Alhazmi

doi:10.3934/math.2021490

AIMS Mathematics

2021, Volume 6, Issue 8: 8453-8465. doi: 10.3934/math.2021490

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Research article

Linear maps on von Neumann algebras acting as Lie type derivation via local actions

1.
Department of Mathematics, Faculty of science and Arts-Rabigh, King Abdulaziz University, KSA
2.
Department of Applied Sciences and Humanities, Jamia Millia Islamia, New Delhi-110025, India
3.
Department of Mathematics, Faculty of science, King Abdulaziz University, Jeddah, KSA

Received: 05 March 2021 Accepted: 19 May 2021 Published: 02 June 2021
MSC : 47B47, 47L10

Let $ \aleph $ be a factor von Neumann algebra with $ dim > 1 $ that operates on a Hilbert space. Within the manuscript, we let out the characterization of Lie type derivation on factor von Neumann algebra of zero product as well as at projection product and notice that it has standard form.
- derivation,
- Lie derivation,
- von Neumann algebra
Citation: Mohd Arif Raza, Aisha Jabeen, Abdul Nadim Khan, Husain Alhazmi. Linear maps on von Neumann algebras acting as Lie type derivation via local actions[J]. AIMS Mathematics, 2021, 6(8): 8453-8465. doi: 10.3934/math.2021490

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Abstract

Let $ \aleph $ be a factor von Neumann algebra with $ dim > 1 $ that operates on a Hilbert space. Within the manuscript, we let out the characterization of Lie type derivation on factor von Neumann algebra of zero product as well as at projection product and notice that it has standard form.

References

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