Journal of Operator Theory

Volume 54, Issue 2, Fall 2005 pp. 229-238.

Some characterizations of weakly compact operators on $H^\infty$ and on the disk algebra. Application to composition operators

Authors: P. Lefevre
Author institution: Universit\'e d'Artois, Facult\'e Jean Perrin, rue Jean Souvraz, S.P. 18, 62307 Lens cedex, France

Summary: We characterize weakly compact operators from $H^\infty$ or from $A(\mathbb{D})$ in terms of absolutely continuous operators. From this, we easily obtain that weakly compact composition operators on $H^\infty$ are compact. We prove the same result for the disk algebra.

Keywords: Composition operator, disk algebra, bounded analytic functions, weakly compact operator.

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