Geodesic
Nest Algebras of Operators and the Dunford-Pettis Property
Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 208-214

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

A Banach space X is said to have the Dunford-Pettis Property if every weakly compact linear operator T: X —> Y, where Y is any Banach space, is completely continuous (that is, T maps weakly convergent sequences to strongly convergent ones). In this paper, we prove that if A is a nest algebra of operators on a separable, infinite dimensional Hilbert space, then A fails to have the Dunford-Pettis Property. We also investigate a certain algebra associated to A, analogous to a construction used by Bourgain and others in connection with the Dunford-Pettis Property for function algebras. We show that this algebra must lie between A and the quasi-triangular algebra A + K and we give examples to show that either extreme or something in between is possible. Finally, we consider the algebra of analytic Toeplitz operators and give a result for the corresponding associated algebra which is analogous to a result of Cima, Jansen, and Yale for H ∞.
DOI : 10.4153/CMB-1991-033-7
Mots-clés : 47D25, 46B20. 
Feeman, Timothy G. Nest Algebras of Operators and the Dunford-Pettis Property. Canadian mathematical bulletin, Tome 34 (1991) no. 2, pp. 208-214. doi: 10.4153/CMB-1991-033-7
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