Journal of Operator Theory

Volume 33, Issue 1, Winter 1995 pp. 33-42.

Weak sequential convergence in the dual of an algebra of compact operators

Authors: Scott W. Brown
Author institution:Department of Mathematics, Indiana University, Bloomington, Indiana 47405-4301, U.S.A.

Summary: It is shown that under certain mild conditions the dual of a commutative algebra of compact operators has the Schur property. This result is then applied to the algebra $H^\infty / \varphi H^\infty$ where $H^\infty$ is the algebra of bounded analytic functions on the disc, and $\varphi$ is an inner function.

Keywords: Schur property, compact operator, Hilbert space operators.

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