Compact multipliers on spaces of analytic functions

Abstract

In the paper compact multiplier operators $$M_{\lambda}: X \rightarrow E$$ from Banach spaces of analytic functions on the unit disk into Banach sequence lattices are studied. If $$H_{\infty} \hookrightarrow X \hookrightarrow H_{2}$$ , then the characterization of compact multipliers is obtained through calculating the Hausdorff measure of noncompactness of diagonal operators between Banach sequence lattices. Furthermore, in the general case $$H_{\infty} \hookrightarrow X \hookrightarrow H_{1}$$ , necessary and sufficient conditions for compactness are presented.