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ISSN 1079-6762

A strongly diagonal power of algebraic order bounded disjointness preserving operators


Authors: Karim Boulabiar, Gerard Buskes and Gleb Sirotkin
Journal: Electron. Res. Announc. Amer. Math. Soc. 9 (2003), 94-98
MSC (2000): Primary 47B65, 06F20, 06F25
Published electronically: October 8, 2003
MathSciNet review: 2029470
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Abstract: An order bounded disjointness preserving operator $T$ on an Archimedean vector lattice is algebraic if and only if the restriction of $T^{n!}$ to the vector sublattice generated by the range of $T^{m}$ is strongly diagonal, where $n$is the degree of the minimal polynomial of $T$ and $m$ is its `valuation'.


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Additional Information

Karim Boulabiar
Affiliation: IPEST, Université de Carthage, BP 51, 2070-La Marsa, Tunisia
Email: karim.boulabiar@ipest.rnu.tn

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

Gleb Sirotkin
Affiliation: Department of Mathematics, Northern Illinois University, DeKalb, IL 60115
Email: sirotkin@math.niu.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-03-00116-1
PII: S 1079-6762(03)00116-1
Keywords: Algebraic, disjointness preserving, locally algebraic, minimal polynomial, orthomorphism, strongly diagonal
Received by editor(s): June 18, 2003
Published electronically: October 8, 2003
Additional Notes: The first and the second authors gratefully acknowledge support from the NATO Collaborative Linkage Grant #PST.CLG.979398. The second author also acknowledges support from the Office of Naval Research Grant #N00014-01-1-0322
Communicated by: Svetlana Katok
Article copyright: © Copyright 2003 American Mathematical Society