Journal of Operator Theory

Volume 34, Issue 2, Fall 1995 pp. 251-261.

A note on the reflexivity of weakly closed subspaces of operators

Authors: Chafiq Benhida
Author institution:URA CNRS 751, UFR de Mathématiques, Université de Lille I, 59655 Villeneuve d'Ascq Cedex, FRANCE

Summary: Many results connect reflexivity and systems of simultaneous equations in the predual $($well known by Property $(\mathbb A_{m,n})$ and $(\mathbb B_{m,n})$) of weakly*-closed subspaces of operators on Hilbert space $($[4], [6] and [9]$)$. Here we prove under a suitable hypothesis on the dual space $\mathcal A$ $($weak*-closed subspace of $\mathcal L(\mathcal H)$$)$ that the dual space generated by $\mathcal A$ and a compact operator $K$ is reflexive if the rank of $K$ is greater than 5.

Keywords: Dual space, predual, property $(\mathbb A_{m,n})$, reflexivity.

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