Fejer's approximation of continuous functions of unitary operators

Abstract

This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions of unitary operators. Starting from a given unitary operator we give a family of sequences of trigonometric polynomials converging weakly to the complex measures which allow us to define functions of the operator.

arXiv commentIn this paper there is a proof, on an approximating character, of the spectral theorem for unitary operators. It was published in Commentationes Mathematicae XLII (2)(2002)