The Simplest Schemes of Generalized Solution of Linear Operator Equation

Abstract

The purpose of Chap. 2 is to give a natural definition of generalized solution of non-solvable linear operator equation in Banach spaces. In Sects. 2.1–2.4 two concepts of generalized solutions are proposed: strong generalized solution and weak generalized solution based on the duality. In Sect. 2.5 the theorem on existence of a weak generalized solution is proved. The relation between these two approaches is studied in Sect. 2.6 in the case of equations with linear injective operator.