Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions

Bonet, José ; Dománski, Paweł ; Lindström, Mikael

Canadian mathematical bulletin, Tome 42 (1999) no. 2, pp. 139-148

Résumé

Every weakly compact composition operator between weighted Banach spaces $H_{v}^{\infty }$ of analytic functions with weighted sup-norms is compact. Lower and upper estimates of the essential norm of continuous composition operators are obtained. The norms of the point evaluation functionals on the Banach space $H_{v}^{\infty }$ are also estimated, thus permitting to get new characterizations of compact composition operators between these spaces.

Détail

DOI : 10.4153/CMB-1999-016-x

Mots-clés : 47B38, 30D55, 46E15, weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator

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