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

Construction of some non-associative algebras from Associative Algebras  with an endomorphism operator, a differential operator or a left averaging  operator