Compact operators in the class $\left( {bv_k^\theta ,bv} \right)$

Abstract

The space $bv$ of bounded variation sequence plays an important role in the summability. More recently this space has been generalized to the space $bv_k^\theta $ and the class $\left( bv_{k}^{\theta },bv\right) $ of infinite matrices has been characterized by Hazar and Sarıgöl [2]. In the present paper, for $1<k<\infty ,$ we give necessary and sufficient conditions for a matrix in the same class to be compact, where $ \theta $ is a sequence of positive numbers.