Compact multipliers on spaces of analytic functions

In the paper compact multiplier operators from Banach spaces of analytic functions on the unit disk into Banach sequence lattices are studied. If , 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 , necessary and sufficient conditions for compactness are presented. Received: 12 August 2008, Revised: 11 January 2009