D(A) and R(A) will be used to denote the domain and range of A, respec The letter H is reserved for a Hilbert space, while the math-script font be used for a RKHS. The duality pairing will be denoted by x, x* , X, x* X*, and the inner product in a Hilbert space H will be denoted

Let X and Y be normed spaces, and B : X Y a linear operator. We will call a normed space X an n – space if the elements of X are func tions f : T R, the set T being arbitrary, and if the topological dual X* contains functionals, i.e., the functionals t, t T for which x, t = x(t), x X. If the space Y is an n – space, and the operator B : X Y is such that all delta functionals in Y* belong to the domain of its dual oper ator B* : Y* X*, then B will be called an a – operator. Since the dual of a continuous linear operator on a normed space is continuous, it follows that every continuous linear operator from a normed space X into an n – space Y is an a – operator. A basic example of an n – space is the space C ([a, b]) of continuous functions on the closed interval [a, b]. It is clear from the reproducing property that any RKHS is an n – space as well.