International Journal of Nonlinear Analysis and Applications

Maps preserving strong Jordan multiple ∗-product on ∗-algebras

Document Type : Research Paper

Author

Department of Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, P. O. Box 47416-1468, Babolsar, Iran

Abstract

Let A be an arbitrary ∗-algebra with unit I over the real or complex field F that contains a nontrivial idempotent P1 and n≥1 a natural number and φ:A⟶A be a surjective map on A such that φ satisfies condition
φ(P)∙n−1φ(P)∙φ(A)=P∙n−1P∙A,
 for every A∈A and projection P∈{P1, I−P1}, where A∙n−1A with repeat n−1 times A is the Jordan multiple ∗-product.   Then φ(A)=φ(I)A for all A∈A and φ(I)2=I.

Keywords

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International Journal of Nonlinear Analysis and Applications
Volume 13, Issue 2
July 2022
Pages 221-225
  • Receive Date: 07 January 2020
  • Revise Date: 28 August 2021
  • Accept Date: 30 August 2021