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On $3$-graded Lie algebras, Jordan pairs and the canonical kernel function
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## On $3$-graded Lie algebras, Jordan pairs and the canonical kernel function

### M. P. de Oliveira

**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. 142-151
- Publisher Identifier: S 1079-6762(03)00122-7
- 2000
*Mathematics Subject Classification*. Primary 32M15; Secondary 22E46, 46E22
*Key words and phrases*. Bergman kernel, symmetric domain, $3$-graded Lie algebra
- Received by editors October 11, 2001
- Received by editors in revised form October 6, 2003
- Posted on December 17, 2003
- Communicated by Efim Zelmanov
- Comments (When Available)

**M. P. de Oliveira**

Department of Mathematics, University of Toronto, Canada

*E-mail address:* `mpdeoliv@math.toronto.edu`

The author has been partially supported by FAPESP.

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