2021/07/25 by Ayupov, Sh. A., Arzikulov, F. N., Umrzaqov, N. M. +1
#16W25 #17C65 #46L57 #47B47 #FOS: Mathematics #Operator Algebras (math.OA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2108.03993
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.