International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 585-588
doi:10.1155/S0161171288000705
Matrix transformations and convex spaces
Ivor J. Maddox
Department of Pure Mathematics, Queen's University of Belfast, Belfast BT7 INN, Ireland
Abstract
In a Hausdorff topological linear space we examine relations between r-convexity and a condition on matrix transformations between null sequences. In particular, for metrizable spaces the condition implies r-convexity. For locally bounded spaces the condition implies sequential completeness.