Spectral Theory in Hilbert Space

Abstract

The aim of this paper is to find (cf. Theorems 4.2; 4.3) a canonical form, and a complete set of invariants, for self-adjoint transformations in a Hilbert space-up to unitary equivalence. While the basic mode of approach is essentially the same as in the excellent exposition in Halmos [1], the final result will be seen to be very much simpler. We do not have to work with the fairly involved concepts of rows, columns, etc.