The second nonlinear mixed Lie triple derivations on standard operator algebras-Reference-Cited by-同舟云学术

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The second nonlinear mixed Lie triple derivations on standard operator algebras

Published:2023-11-20 Issue:0 Volume:0 Page:
ISSN:1072-947X
Container-title:Georgian Mathematical Journal
language:en
Short-container-title:

Author:

Rehman Nadeem ur¹^ORCID,Nisar Junaid²^ORCID,Wani Bilal Ahmad³^ORCID

Affiliation:

1. Department of Mathematics , Aligarh Muslim University , Aligarh - 202002 , India

2. Department of Applied Mathematics , Symbiosis Institute of Technology , Symbiosis International University , Pune - 412115 , India

3. Department of Mathematics , University of Kashmir , Srinagar - 190006 , India

Abstract

Abstract Let 𝒜

{\mathcal{A}}

be a standard operator algebra containing the identity operator I on an infinite dimensional complex Hilbert space ℋ

{\mathcal{H}}

which is closed under adjoint operation. Suppose that ϕ : 𝒜 → 𝒜

{\phi:\mathcal{A}\to\mathcal{A}}

is the second nonlinear mixed Lie triple derivation. Then ϕ is an additive ∗

{\ast}

-derivation.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/gmj-2023-2086/pdf

Reference12 articles.

1. R. L. An and J. C. Hou, A characterization of ∗ \ast -automorphism on ℬ ⁢ ( H ) \mathcal{B}(H) , Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 2, 287–294.

2. Z. Bai and S. Du, Maps preserving products X ⁢ Y - Y ⁢ X ∗ XY-YX^{\ast} on von Neumann algebras, J. Math. Anal. Appl. 386 (2012), no. 1, 103–109.

3. J. Cui and C.-K. Li, Maps preserving product X ⁢ Y - Y ⁢ X * XY-YX^{*} on factor von Neumann algebras, Linear Algebra Appl. 431 (2009), no. 5–7, 833–842.

4. P. R. Halmos, A Hilbert Space Problem Book, 2nd ed., Encyclopedia Math. Appl. 17, Springer, New York, 1982.

5. D. Huo, B. Zheng, J. Xu and H. Liu, Nonlinear mappings preserving Jordan multiple * * -product on factor von Neumann algebras, Linear Multilinear Algebra 63 (2015), no. 5, 1026–1036.

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