It is known that the calculus with functions of operators is defined by a class \({\mathcal A}\) of operators in a Banach space \({\mathcal B}\) and by an algebra F of scalar functions of real or complex variable with aid of the homomorphism \(f\mapsto f(A)\) of the algebra F in the algebra \({\mathcal L}({\mathcal B})\) of bounded linear mappings of \({\mathcal B}\), \(A\in {\mathcal A}\). In the present paper the author gives a way for the enlargement of the class \({\mathcal A}\) with which on has started in the construction of a functional calculus for functions of operators. Namely, if the operators A, B belong to the class \({\mathcal A}\), the operator \(A+B\) in general does not belong. The author gives a way that ensures to confer a sense to \(f(A+B)\) and therefore the class \({\mathcal A}\) is enlarged. Of course, the paper contains more other contributions to operator functional calculus, the author having a world-wide fame in this domain. For technical reasons we are not able to reproduce these contributions.