2-Local derivations of real AW*-algebras are derivation

Abstract

2-Local derivations on real matrix algebras over unital semi-prime Banach algebras are considered. Using the real analogue of the result that any 2-local derivation on the algebra M_{2^n}(A) (nge 2) is a derivation, it is shown that any 2-local derivation on real AW^*-algebra for which the enveloping algebra is (complex) AW*-algebra, is a derivation, where A is a unital semi-prime Banach algebra with the inner derivation property.