On the spaces ℬ𝒱𝜗0 of double sequences of bounded variation

Abstract

In this paper, we introduce the new spaces [Formula: see text] of double sequences of bounded variation, where [Formula: see text], and we investigate some topological properties. Moreover, we prove some strict inclusion relations and we examine [Formula: see text]-dual of the spaces [Formula: see text]. Finally, we characterize some classes of four-dimensional matrices [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text].