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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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