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An order bounded disjointness preserving operator $T$ on an Archi\-medean 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 `\textit{valuation}'.

Copyright 2003 American Mathematical Society

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Article Info

• ERA Amer. Math. Soc. 09 (2003), pp. 94-98
• Publisher Identifier: S 1079-6762(03)00116-1
• 2000 Mathematics Subject Classification. Primary 47B65, 06F20, 06F25
• Key words and phrases. Algebraic, disjointness preserving, locally algebraic, minimal polynomial, orthomorphism, strongly diagonal
• Received by editors June 18, 2003
• Posted on October 8, 2003
• Communicated by Svetlana Katok
• Comments (When Available)

Karim Boulabiar

IPEST, Université de Carthage, BP 51, 2070-La Marsa, Tunisia

E-mail address: karim.boulabiar@ipest.rnu.tn

Gerard Buskes

Department of Mathematics, University of Mississippi, MS 38677

E-mail address: mmbuskes@olemiss.edu

Gleb Sirotkin

Department of Mathematics, Northern Illinois University, DeKalb, IL 60115

E-mail address: sirotkin@math.niu.edu

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.