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Sequential closedness of Boolean algebras of projections in Banach spaces

100%

Fremlin D., de Pagter B., Ricker W.

Studia Mathematica

2005

tom 167

nr 1

45-62

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).

Schauder decompositions and multiplier theorems

100%

Clément P., de Pagter B., Sukochev F. A., Witvliet H.

Studia Mathematica

2000

tom 138

nr 2

135-163

We study the interplay between unconditional decompositions and the R-boundedness of collections of operators. In particular, we get several multiplier results of Marcinkiewicz type for $L^p$-spaces of functions with values in a Banach space X. Furthermore, we show connections between the above-mentioned properties and geometric properties of the Banach space X.

Ograniczanie wyników

2 Studia Mathematica

2 de Pagter B.

1 Clément P.

1 Fremlin D.

1 Ricker W.

1 Sukochev F. A.

1 Witvliet H.

1 2005

1 2000

Wyniki wyszukiwania

Sequential closedness of Boolean algebras of projections in Banach spaces

Schauder decompositions and multiplier theorems