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On density with respect to equivalent measures

Bartosiewicz A., Filipczak M., Poreda T.

Demonstratio Mathematica

2010

Vol. 43, nr 1

21-28

In the paper there is disscussed a notion of a density point of a Borel subset of a metric space with respect to a Borel measure(mikro) . There are considered densities with respect to equivalent measures and density with respect to the limit of a sequence of equivalent measures.

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.