ABSTRACT
The concept of ‘adjoint operator’ is widely used in the theory of differential equations for a formally adjoint operator which often governs just a sequence of differentiation operators. In the context of functional analysis, the definition of the adjoint operator is more sophisticated and essentially depends on boundary conditions. But to introduce an adjoint operator and the corresponding adjoint equation one needs first to formulate the concept of ‘dual space’. It turns out that, in doing so, there exist several possibilities at our disposal. To make clear how the adjoint operators and equations are treated in the subsequent text we give the definition of the dual space, beginning with the case of Banach spaces.
