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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

Texto completo disponible sólo en PDF

Full text available only in PDF format.

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

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