Spectral Stieltjes-Type Integration and Some Applications

Details Spectral Stieltjes-Type Integration and Some Applications Spectral Stieltjes-Type Integration and Some Applications

2005-11-25

arxiv.org/abs/math/0511637v2

Mathematics

Functional Analysis

This paper has been withdrawn by the author. This paper has been substantially rewritten

Scientific paper

This paper presents Stieltjes-type integration for operator-valued functions with respect to spectral families. The relation between Riemann-Stieltjes integrals associated with some classes of spectral families including, in particular, those that arise in the context of the Stone representation theorem for Banach spaces is established. The developed approach is applied to the structural analysis of the operators commuting with a one-parameter representation satisfying the Generalized Stone theorem.

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