On characteristic and adjoint elements of linear operators

Abstract

The aim of the present paper is to show that with certain assumptions a system of characteristic and adjoint elements of a linear operator can be so chosen that the Gram matrix of this system is finite and has a finite reciprocal matrix. A system of elements with such a Gram matrix will be called normal. Problems of expansion in such systems are solved quite simply and many propositions in the theory of linear equations with non-selfconjugate operators are formulated in almost the same way as in the theory of equations with self-conjugate operators.