Article ID Journal Published Year Pages File Type
4616587 Journal of Mathematical Analysis and Applications 2013 6 Pages PDF
Abstract

Let AA be a unital C∗C∗-algebra and A″A″ its second dual. By σ(a)σ(a) and r(a)r(a) we denote the spectrum and the spectral radius of a∈Aa∈A, respectively. The following two statements hold for arbitrary a,b∈Aa,b∈A: (1) σ(ac)⊆σ(bc)∪{0}σ(ac)⊆σ(bc)∪{0} for every c∈Ac∈A if and only if there exists a central projection z∈A″z∈A″ such that a=zba=zb, (2) r(ac)≤r(bc)r(ac)≤r(bc) for every c∈Ac∈A if and only if there exists a central element zz in A″A″ such that a=zba=zb and ‖z‖≤1‖z‖≤1.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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