# 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 MathÃ©matiques et Informatique, Universite Bordeaux I, 351, Cours de la Liberation, 33405 Talence Cedex, FRANCE Current address: Universite des Sciences et Technologies de Lille, U.F.R. de Mathematiques Pures et Appliquees, 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).

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