Approximately order zero maps between C*-algebras

2019/11/05 by Kochanek, Tomasz
#46L05 #46L85 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.1911.01689

Abstract

We investigate linear operators between C^∗-algebras which approximately preserve involution and orthogonality, the latter meaning that for some ε>0 we have ‖ϕ(x)ϕ(y)‖≤ε‖x‖‖y‖ for all positive x,y with xy=0. We establish some structural properties of such maps concerning approximate Jordan-like equations and almost commutation relations. In some situations (e.g. when the codomain is finite-dimensional), we show that ϕ can be approximated by an approximate Jordan ^∗-homomorphism, with both errors depending only on ‖ϕ‖ and ε.

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