Local triple derivations on real C*-algebras and JB*-triples
Francisco J. Fern\'andez-Polo, Alexis Molino, and Antonio M. Peralta
TL;DR
This paper investigates conditions under which local triple derivations on real JB*-triples are actual triple derivations, providing examples and sufficient conditions to distinguish between the two.
Contribution
It offers the first known example of a local triple derivation that is not a triple derivation on a real JB*-triple and establishes criteria ensuring they coincide.
Findings
Example of a local triple derivation not being a triple derivation.
Sufficient conditions for local triple derivations to be triple derivations.
Analysis of rank-one Cartan factors of type I.
Abstract
We study when a local triple derivation on a real JB*-triple is a triple derivation. We find an example of a (real linear) local triple derivation on a rank-one Cartan factor of type I which is not a triple derivation. On the other hand, we find sufficient conditions on a real JB*-triple E to guarantee that every local triple derivation on E is a triple derivation.
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Taxonomy
TopicsAdvanced Topics in Algebra · Advanced Differential Geometry Research · Matrix Theory and Algorithms