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.

Keywords

• Matrix transformations,Sequence spaces,$bv_{k}^{\theta }$ spaces

Kaynakça

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