# Sequential closedness of Boolean algebras of projections in Banach spaces

D. H. Fremlin; B. de Pagter; W. J. Ricker

Studia Mathematica (2005)

- Volume: 167, Issue: 1, page 45-62
- ISSN: 0039-3223

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topD. H. Fremlin, B. de Pagter, and W. J. Ricker. "Sequential closedness of Boolean algebras of projections in Banach spaces." Studia Mathematica 167.1 (2005): 45-62. <http://eudml.org/doc/285116>.

@article{D2005,

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).},

author = {D. H. Fremlin, B. de Pagter, W. J. Ricker},

journal = {Studia Mathematica},

keywords = {Boolean algebras of projections; sequential closedness; Bade functionals; band projections; spaces of measures},

language = {eng},

number = {1},

pages = {45-62},

title = {Sequential closedness of Boolean algebras of projections in Banach spaces},

url = {http://eudml.org/doc/285116},

volume = {167},

year = {2005},

}

TY - JOUR

AU - D. H. Fremlin

AU - B. de Pagter

AU - W. J. Ricker

TI - Sequential closedness of Boolean algebras of projections in Banach spaces

JO - Studia Mathematica

PY - 2005

VL - 167

IS - 1

SP - 45

EP - 62

AB - 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).

LA - eng

KW - Boolean algebras of projections; sequential closedness; Bade functionals; band projections; spaces of measures

UR - http://eudml.org/doc/285116

ER -

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