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Sequential closedness of Boolean algebras of projections in Banach spaces

Authors :
Werner J. Ricker
B. de Pagter
David H. Fremlin
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