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International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 3, Pages 585-588
http://dx.doi.org/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

Copyright © 1988 Hindawi Publishing Corporation. 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.