Linear maps preserve the covariance sets

2018/01/14 by Mohammad Hossein Alizadeh, Alizadeh, Mohammad Hossein
Computer Science · Mathematics · #47H04 #47H05 #49J53 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.1801.04519

openalex publication_date 2018/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A and B are C^{\huge ∗}% -algebras. A linear map ϕ:A→ B is C^∗-Jordan homomorphism if it is a Jordan homomorphism which preserves the adjoint operation. In this note we show that C^∗-Jordan homomorphisms -- under mild assumptions -- preserving covariance set and covariance coset in C^∗-algebras.

Related

• Linear maps between C*-algebras that are *-homomorphisms at a fixed point
• Invertibility preserving mappings onto finite C*-algebras
• Linear maps between C*-algebras whose adjoints preserve extreme points\n of the dual ball
• Weighted homomorphisms between C*-algebras
• Non-linear characterization of Jordan *-isomorphisms via maps on positive cones of C^*-algebras