2-Local and local derivations on Jordan matrix rings over commutative involutive rings

N. M. Umrzaqov, Author name not available (Why is that?), Farkhad Nematjonovich Arzikulov, Sh. A. Ayupov

Publication date: 25 July 2021

Abstract: In the present paper we prove that every 2-local inner derivation on the Jordan ring of self-adjoint matrices over a commutative involutive ring is a derivation. We also apply our technique to various Jordan algebras of infinite dimensional self-adjoint matrix-valued maps on a set and prove that every 2-local spatial derivation on such algebras is a spatial derivation. It is also proved that every local spatial derivation on the same Jordan algebras is a derivation.

Mathematics Subject Classification ID

Commutators, derivations, elementary operators, etc. (47B47) Derivations, actions of Lie algebras (16W25) Jordan structures on Banach spaces and algebras (17C65) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57)

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