Sequential closedness of Boolean algebras of projections in Banach spaces

• Autorzy: D. H. Fremlin , B. de Pagter , W. J. Ricker
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.
• 46B26: Nonseparable Banach spaces
• 46E27: Spaces of measures
• 46B42: Banach lattices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 167
• Numer: 1
• Strony: 45-62

Daty

wydano

2005

Twórcy

autor

D. H. Fremlin

• Department of Mathematics, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom

autor

B. de Pagter

• Department of Applied Mathematical Analysis, Faculty EEMCS, Delft University of Technology, Mekelweg 4, 2628CD Delft, The Netherlands

autor

W. J. Ricker

• Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt-Ingolstadt, D-85071 Eichstätt, Germany

Identyfikatory

DOI

10.4064/sm167-1-4