Sequential closedness of Boolean algebras of projections in Banach spaces
D. H. Fremlin, B. de Pagter, W. J. Ricker (2005)
Studia Mathematica
Similarity:
Complete and σ-complete Boolean algebras of projections acting in a Banach space were introduced by W. Bade in the 1950's. A basic fact is that every complete Boolean algebra of projections is necessarily a closed set for the strong operator topology. Here we address the analogous question for σ-complete Boolean algebras: are they always a sequentially closed set for the strong operator topology? For the atomic case the answer is shown to be affirmative. For the general case, we develop...