Topological function-theoretic proofs in spectral theory

In this paper, the spectral theorem and related characterizations of the spectrum and the spectral projections for bounded self adjoint and normal operators on a Hilbert space, are proved in purely topological —function theoretic terms. The basis for such a development, is the Gelfand—Naimark theorem for commutativeC ^*-algebras and the fact that the structure space of the (abelian) von Neumann algebra generated by the operator is a Stonean space.