On the concept of generalized solution of operator equations in banach spaces - Petunin, Yu. I. (Ukrains’kyi Matematychnyi Zhurnal, 1996)
We introduce a new concept of generalized solution of operator equations with closed linear operator in a Banach space as an element of the completion of the space in certain locally convex topology. We prove a theorem on the existence and uniqueness of a generalized solution and give examples of finding the generalized solution for infinite systems of the linear algebraic equations.