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2-Local and local derivations on Jordan matrix rings over commutative involutive rings (2108.03993v2)
Published 25 Jul 2021 in math.RA and math.OA
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.