On the commutant of the ideal centre


Abstract


The centre Z(E) of a Riesz space E is the collection of all operators T on E that satisfy -λ I≤ T≤λ I for some λ ∈ R, where I is the identity operator. We study the commutant Z(E)_C of Z(E) in the order bounded operators on E. If E is a Riesz space with topologically full centre, we identify Z(E)_C with the orthomorphisms of E.

DOI Code: 10.1285/i15900932v18n1p63

Keywords: Riesz space; Ideal center; Commutant; Orthomorphisms

Classification: 46A40

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