Linear maps and covariance sets

Document Type : Research Paper

Author
Mohammad Hossein Alizadeh 1, 2
1 Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
2 Department of Mathematics, Islamic Azad University, Nur Branch, Nur, Iran
10.22075/ijnaa.2020.19469.2081
Abstract
Let $\mathcal{A}$ and $\mathcal{B}$\ are $C^{{\ast}} $-algebras. A linear map $\phi:\mathcal{A\rightarrow B}$ is $C^{\ast}$-Jordan homomorphism if it is a Jordan homomorphism which preserves the adjoint operation. In this note we show that $C^{\ast}$-Jordan homomorphisms -under mild assumptions- preserving covariance set and covariance coset in $C^{\ast}$-algebras.
Keywords
Moore-Penrose inverse
covariance set
Jordan homomorphism
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[2] M. H. Alizadeh, On the covariance of generalized inverse in C∗-algebra, J. Numer. Anal. Indust. Appl. Math. 5(2011) 135–139.
[3] N. Boudi and M. Mbekhta, Additive maps preserving strongly generalized inverses, J. Operator Theory, 64 (2010) 117- 130.
[4] M. Eshaghi Gordji, n-Jodan homomorphisms, Bull. Aust. Math. Soc. 80 (2009) 15.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 495-497

  • Receive Date 16 October 2019
  • Revise Date 05 January 2020
  • Accept Date 28 January 2020

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