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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polar decomposition of order bounded disjointness preserving operators


Authors: Karim Boulabiar and Gerard Buskes
Journal: Proc. Amer. Math. Soc. 132 (2004), 799-806
MSC (2000): Primary 46A40, 47B65
Published electronically: August 21, 2003
MathSciNet review: 2019958
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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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Karim Boulabiar
Affiliation: Département de Mathématiques, Faculté des Sciences de Bizerte, Université de 7 Novembre à Carthage, 7021-Zarzouna, Tunisia
Email: karim.boulabiar@ipest.rnu.tn

Gerard Buskes
Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
Email: mmbuskes@olemiss.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07007-2
PII: S 0002-9939(03)07007-2
Keywords: Polar decomposition, disjointness preserving operator, lattice homomorphism, orthomorphism, complex Riesz space
Received by editor(s): February 20, 2002
Received by editor(s) in revised form: July 29, 2002, and October 30, 2002
Published electronically: August 21, 2003
Additional Notes: The second named author gratefully acknowledges support from the Department of the Navy, Office of Naval Research Grant, no.\ N00014-01-1-0322
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society