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- W1970575941 abstract "Let A be a Banach algebra and let B be a linear subspace of A. Recall that A has the Dunford Pettis property if whenever ƒ n → 0 weakly in A* and φn → 0 weakly in A* then φn(ƒ n ) → 0. Bourgain showed that H ∞ has the Dunford Pettis property using the theory of ultraproducts. The Dunford Pettis property is related to the notion of Bourgain algebra, denoted B b , introduced by [6] Cima and Timoney. The algebra B b is the set of ƒ in A such that if ƒ n → 0 weakly in B then dist(ƒƒ n , B ) —> 0. Bourgain showed [2] that a closed subspace X of C(L)y where L is a compact Hausdorff space, has the Dunford Pettis property if X b — C(L). Cima and Timoney proved that Bb is a closed subalgebra of A and that if B is an algebra then B ⊂ B b . In this paper we study the Bourgain algebra associated with various algebras of functions on the unit circle T." @default.
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- W1970575941 date "1992-08-01" @default.
- W1970575941 modified "2023-09-27" @default.
- W1970575941 title "Bourgain Algebras of Douglas Algebras" @default.
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- W1970575941 doi "https://doi.org/10.4153/cjm-1992-047-6" @default.
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