Journal of Operator Theory

Volume 34, Issue 1, Summer 1995 pp. 3-16.

On the extension of the properties $(\mathbb A_{m,n})$

Authors: Chafiq Benhida
Author institution:UFR de Mathématiques et Informatique, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, FRANCE Current address: Université des Sciences et Technologies de Lille, U.F.R. de Mathématiques Pures et Appliquées, 59655 Villeneuve d’Ascq Cedex, FRANCE

Summary: Here we show that we can extend the properties $(\mathbb A_{m,n})$ from a given weak*-closed subspace to a larger one in some cases. Our technique yields examples of weak*-closed subspaces $\mathcal A$ having the property $(\mathbb A_{\aleph N_0})$ without having any of the properties $X_{0,\gamma }$, in contrast to the case where $\mathcal A$ is the dual algebra generated by a contraction in the class $\mathbb A$ (for which it is well known that the two properties are equivalent).

Keywords: Dual algebra, weak*-closed subspace, compact operator, property $(\mathbb A_{m,n})$.

Contents Full-Text PDF