Non-linear new product A ∗ B − B ∗ A derivations on ∗-algebras

Taghavi, A.; Razeghi, M.; Taghavi, A.; Razeghi, M.

doi:10.22199/issn.0717-6279-2020-02-0029

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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.2 Antofagasta Apr. 2020

http://dx.doi.org/10.22199/issn.0717-6279-2020-02-0029

Artículos

Non-linear new product A ^∗ B − B ^∗ A derivations on ∗-algebras

A. Taghavi¹
http://orcid.org/0000-0001-6230-733X

M. Razeghi²

^¹University of Mazandaran, Dept. of Mathematics, Faculty of Mathematical Sciences, Babolsar, Iran. e-mail: taghavi@umz.ac.ir

^² University of Mazandaran, Dept. of Mathematics, Faculty of Mathematical Sciences, Babolsar, Iran. e-mail: razeghi.mehran19@yahoo.com

Abstract

Let A be a prime ∗-algebra with unit I and a nontrivial projection. Then the map Φ : A → A satisfies in the following condition

Φ(A ⋄ B) = Φ(A) ⋄ B + A ⋄ Φ(B)

where A⋄ B = A∗B −B∗A for all A, B ∈ A, is additive. Moreover, if Φ(αI) is self-adjoint operator for α ∈ {1, i} then Φ is a ∗-derivation.

Keywords: New product derivation: Prime ∗-algebra; Additive map

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Acknowledgments

The authors would like to thank anonymous referee for a thorough and detailed report with many helpful comments and suggestions.

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Received: June 30, 2019; Accepted: July 30, 2019

Article copyright: © 2020 A. Taghavi and M. Razeghi. This is an open access article distributed under the terms of the Creative Commons Licence, which permits unrestricted use and distribution provided the original author and source are credited.

This is an open-access article distributed under the terms of the Creative Commons Attribution License