Representation of strongly truncated Riesz spaces

2019/10/25 by Boulabiar, Karim, Hajji, Rawaa
#46A40 #46B40 #47B65 #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)

paper · doi:10.48550/arxiv.1910.11687

Abstract

Following a recent idea by Ball, we introduce the notion of strongly truncated Riesz space with a suitable spectrum. We prove that, under an extra Archimedean type condition, any strongly truncated Riesz space is isomorphic to a uniformly dense Riesz subspace of a C₀( X) -space. This turns out to be a direct generalization of the classical Kakutani Representation Theorem on Archimedean Riesz spaces with strong unit. Another representation theorem on normed Riesz spaces, due to Fremlin, will be obtained as a consequence of our main result.

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