Norms and compactness of operators on absolute weighted mean summable series

Abstract

In a recent paper [16], we characterized the classes of triangular matrix transformations mapping the spaces INpI and INqIk into the spaces INqIk and INqI, respectively, where the space INpIk, of series summable by absolute summability method. In the present paper we show that each element of these classes corresponds to a bounded linear operators, and determine exactly or obtain estimates for their norms and those in some well konown classes. Also, we characterized compact opğerators in these classes by using Housdorff measue noncompactness.

Keywords

• Absolute weighted summability
• bounded operator
• compact operator
• Hausdorff measure of non compactness
• matrixtrans formations.