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Sequential closedness of Boolean algebras of projections in Banach spaces
- Source :
- Studia Mathematica. 167:45-62
- Publication Year :
- 2005
- Publisher :
- Institute of Mathematics, Polish Academy of Sciences, 2005.
-
Abstract
- 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 criteria which characterize when a σ-complete Boolean algebra of projections is sequentially closed. These criteria are used to show that both possibilities occur: there exist examples which are sequentially closed and others which are not (even in Hilbert space).
Details
- ISSN :
- 17306337 and 00393223
- Volume :
- 167
- Database :
- OpenAIRE
- Journal :
- Studia Mathematica
- Accession number :
- edsair.doi...........350b59786ab06df877653eae23f4d772