International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 585-588
doi:10.1155/S0161171288000705
Matrix transformations and convex spaces
Department of Pure Mathematics, Queen's University of Belfast, Belfast BT7 INN, Ireland
Received 18 March 1988
For Professor Brain Kuttner on His Eightieth Birthday
Copyright © 1988 I. J. Maddox. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.