Linear maps preserve the covariance sets

Mohammad Hossein Alizadeh

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arXiv · 1801.04519

Linear maps preserve the covariance sets

Mohammad Hossein Alizadeh

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Abstract

Let $\mathcal{A}$ and $\mathcal{B}$\ are $C^{{\huge \ast}}% $-algebras\textbf{.} A\textbf{ }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.

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Mohammad Hossein Alizadeh. 2018-01-14. Linear maps preserve the covariance sets. https://arxiv.org/abs/1801.04519

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