Sequences of generalized bounded variation

The purpose of this article is to offer a short, guided tour through the introduction and development of a class of sequence spaces that represent a discretization of spaces of functions of generalized bounded variation. The paths that we follow are motivated by, and parallel, some of those forged over the last 140 years in expanding Jordan’s original concept of functions of bounded variation on a compact interval. In addition, we devote attention to the issue of stability of the sequence spaces under coordinatewise multiplication and also endow them with a canonical norm.