Polar decomposition of order bounded disjointness preserving operators

Boulabiar, Karim; Buskes, Gerard

doi:10.1090/S0002-9939-03-07007-2

Polar decomposition of order bounded disjointness preserving operators
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by Karim Boulabiar and Gerard Buskes PDF

Proc. Amer. Math. Soc. 132 (2004), 799-806 Request permission

Abstract:

We constructively prove (i.e., in ZF set theory) a decomposition theorem for certain order bounded disjointness preserving operators between any two Riesz spaces, real or complex, in terms of the absolute value of another order bounded disjointness preserving operator. In this way, we constructively generalize results by Abramovich, Arensen and Kitover (1992), Grobler and Huijsmans (1997), Hart (1985), Kutateladze, and Meyer-Nieberg (1991).

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