Nonlinear Skew Lie-Type Derivations on ∗-Algebra

Md Arshad Madni (), Amal S. Alali and Muzibur Rahman Mozumder
Additional contact information
Md Arshad Madni: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India
Amal S. Alali: Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
Muzibur Rahman Mozumder: Department of Mathematics, Faculty of Science, Aligarh Muslim University, Aligarh 202002, India

Mathematics, 2023, vol. 11, issue 18, 1-12

Abstract: Let A be a unital ∗-algebra over the complex fields C . For any H 1 , H 2 ∈ A , a product [ H 1 , H 2 ] • = H 1 H 2 − H 2 H 1 * is called the skew Lie product. In this article, it is shown that if a map ξ : A → A (not necessarily linear) satisfies ξ ( P n ( H 1 , H 2 , … , H n ) ) = ∑ i = 1 n P n ( H 1 , … , H i − 1 , ξ ( H i ) , H i + 1 , … , H n ) ( n ≥ 3 ) for all H 1 , H 2 , … , H n ∈ A , then ξ is additive. Moreover, if ξ ( i e 2 ) is self-adjoint, then ξ is ∗-derivation. As applications, we apply our main result to some special classes of unital ∗-algebras such as prime ∗-algebra, standard operator algebra, factor von Neumann algebra, and von Neumann algebra with no central summands of type I 1 .

Keywords: additive ?-derivation; mixed bi-skew Jordan triple derivation; ?-algebras; von Neumann algebra (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/18/3819/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/18/3819/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:18:p:3819-:d:1233658

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().