Integration with respect to Baire vector measures with applications to the spectral theory

  • Marian Nowak

    University of Zielona Gora, Poland
Integration with respect to Baire vector measures with applications to the spectral theory cover

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Abstract

Let be a completely regular Hausdorff space and the space of all bounded continuous scalar functions on , equipped with the strict topology . We develop a general integral representation theory of -continuous linear operators from to a locally convex Hausdorff space . We present equivalent conditions for a -continuous operator to be weakly compact. If is a sequentially complete unital locally convex algebra, we establish an integral representation of a -continuous unital algebra homomorphism . As an application, we develop spectral theory for operators , where denotes the algebra of bounded linear operators of a Banach space into itself, equipped with the topology of simple convergence.

Cite this article

Marian Nowak, Integration with respect to Baire vector measures with applications to the spectral theory. Z. Anal. Anwend. 41 (2022), no. 1/2, pp. 11–35

DOI 10.4171/ZAA/1696