The ideal of Lesieur-Croisot elements of Jordan pairs
Fernando Montaner, Irene Paniello
TL;DR
This paper investigates elements in Jordan pairs whose local algebras are Lesieur-Croisot, establishing that in nondegenerate pairs, these elements form an ideal, thus advancing understanding of Jordan pair structure.
Contribution
It proves that the set of Lesieur-Croisot elements forms an ideal in nondegenerate Jordan pairs, linking local algebra properties to global structure.
Findings
Lesieur-Croisot elements form an ideal in nondegenerate Jordan pairs
Characterization of local Jordan algebras as Lesieur-Croisot algebras
Extension of classical order concepts to Jordan pair theory
Abstract
We study the sets of elements of Jordan pairs whose local Jordan algebras are Lesieur-Croisot algebras, that is, classical orders in nondegenerate Jordan algebras with finite capacity. It is then proved that, if the Jordan pair is nondegenerate, the set of its Lesieur-Croisot elements is an ideal of the Jordan pair.
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Taxonomy
TopicsAdvanced Topics in Algebra · Holomorphic and Operator Theory · Advanced Operator Algebra Research