Integration with respect to Baire vector measures with applications to the spectral theory
Marian NowakUniversity of Zielona Gora, Poland
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. 11–35DOI 10.4171/ZAA/1696