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Polar decomposition of order bounded disjointness preserving operators
Author(s):
Karim
Boulabiar;
Gerard
Buskes
Journal:
Proc. Amer. Math. Soc.
132
(2004),
799-806.
MSC (2000):
Primary 46A40, 47B65
Posted:
August 21, 2003
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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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Additional Information:
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:
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
Posted:
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
Copyright of article:
Copyright
2003,
American Mathematical Society
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