Eine Charakterisierung der Boole'schen Algebra zu einer co -direkten Zerlegung

Abstract

In this paper nuclear Boolean Algebras of projections in a locally convex space are considered. This are Boolean Algebras with special continuity properties, which are shared, for instance, by each bounded Boolean Algebra of projections in an ℒ∞-space and by the algebra of each equicontinuos spectral measure in a nuclear space. It will be shown that a ℴ-complete nuclear Boolean Algebra leads to a co-direct sum of locally convex spaces and all the projections of the algebra belong to the complete algebra of projections of this co-direct partition. On the other hand if in a given locally convex space E there exists a nuclear complete Boolean Algebra of projections which has multiplicity one then each equicontinuos Boolean Algebra of projections in E is nuclear.