Geodesic
Bourgain Algebras of Douglas Algebras
Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 797-804

Voir la notice de l'article provenant de la source Cambridge University Press

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 ƒn→ 0 weakly in A* and φn → 0 weakly in A* then φn(ƒn) → 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 Bb, introduced by [6] Cima and Timoney. The algebra Bb is the set of ƒ in A such that if ƒn → 0 weakly in B then dist(ƒƒn, 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 Xb — C(L). Cima and Timoney proved that Bb is a closed subalgebra of A and that if B is an algebra then B⊂Bb. In this paper we study the Bourgain algebra associated with various algebras of functions on the unit circle T.
DOI : 10.4153/CJM-1992-047-6
Mots-clés : 46J10, 46J30 
Gorkin, Pamela; Izuchi, Keiji; Mortini, Raymond. Bourgain Algebras of Douglas Algebras. Canadian journal of mathematics, Tome 44 (1992) no. 4, pp. 797-804. doi: 10.4153/CJM-1992-047-6
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