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Matrix transformations and convex spaces. (English) Zbl 0653.40003

Summary: 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.

MSC:

40C05 Matrix methods for summability
40J05 Summability in abstract structures
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