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Fejer's approximation of continuous functions of unitary operators

Zajkowski K.

Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae

2002

[Z] 42(2)

261-267

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.