Fejer's approximation of continuous functions of unitary operators

Krzysztof Zajkowski

Fejer's approximation of continuous functions of unitary operators

Functional Analysis 2014-03-11 v1

Authors: Krzysztof Zajkowski

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.

Keywords

fejer approximation unitary operators spectral theory hilbert space trigonometric polynomials continuous functions weak convergence

Cite

@article{arxiv.1403.1979,
  title  = {Fejer's approximation of continuous functions of unitary operators},
  author = {Krzysztof Zajkowski},
  journal= {arXiv preprint arXiv:1403.1979},
  year   = {2014}
}

Comments

In 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)

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