  In this paper, we introduce the concepts of endomorphism operator, left
averaging operator, differential operator and Rota-Baxter Operator, and we
construct examples of these linear maps on associative algebras with a left
identity, a skew-idempotent or an idempotent element. These maps on associative
algebra induce a non-associative algebra structure such as Lie algebra, Pre-Lie
algebra, Jordan algebra, Flexible Algebra or (left) Leibniz algebra. We
consider the construction of non-associative algebras from associative algebras
with Linear Operators as the main results of this work. In this paper we give
examples of non-associative algebras on subspaces of square matrices M3(R).
