The uniformly closed algebra generated by a complete Boolean algebra of projections
The main result established is that the weak operator closed algebra generated by a complete, equicontinuous Boolean algebra of projections in locally convex space X coincides with the closed algebra that it generates with respect to the topology of uniform convergence on the bounded sets of X. For X a Banach space, in which case the topology of uniform convergence on the bounded sets of X is just the uniform operator topology, this is a classical result due to W. G. Bade. The proof of the main result, which is based on the theory of integration with respect to spectral measures, is new even in the Banach space setting.
weak operator closed algebra generated by a complete equicontinuous Boolean algebra of projections in a locally convex space
topology of uniform convergence on the bounded sets
integration with respect to spectral measures
scientific article; zbMATH DE number 4069649
scientific article