Commutative $C^{\ast }$-algebras and $\sigma$-normal morphisms

Abstract

We prove in an elementary fashion that the image of a commutative monotone $\sigma$-complete $C^{\ast }$-algebra under a $\sigma$-normal morphism is again monotone $\sigma$-complete and give an application of this result in spectral theory.

LaTeX, 5 pages, 1 figure. Relation with existing literature clarified