Boundedness of completely additive measures with application to 2-local triple derivations
Jan Hamhalter, Karimbergen Kudaybergenov, Antonio M. Peralta, Bernard, Russo
TL;DR
This paper proves a Jordan version of Dorofeev's boundedness theorem for completely additive measures and demonstrates that every 2-local triple derivation on a continuous JBW*-triple is actually a triple derivation, regardless of linearity or continuity.
Contribution
It introduces a Jordan version of a boundedness theorem and establishes that 2-local triple derivations are genuine triple derivations in continuous JBW*-triples.
Findings
Jordan version of Dorofeev's boundedness theorem proved
Every 2-local triple derivation is a triple derivation in continuous JBW*-triples
Applicable to non-linear and non-continuous cases
Abstract
We prove a Jordan version of Dorofeev's boundedness theorem for completely additive measues and use it to show that every (not necessarily linear nor continuous) 2-local triple derivation on a continuous JBW*-triple is a triple derivation.
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