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A strongly diagonal power of algebraic order bounded disjointness preserving operators
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## A strongly diagonal power of algebraic order bounded disjointness preserving operators

### Karim Boulabiar, Gerard Buskes, and Gleb Sirotkin

**Abstract.**
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.

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