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Full-Completeness in Weighted Spaces

Published online by Cambridge University Press:  20 November 2018

W. H. Summers
W. H. Summers*
Affiliation:
Univesity of Arkansas, Fayetteville, Arkansas
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That the class of fully complete (B-complete) locally convex spaces has an essential role has been well-established (see, e.g., Collins [2], Husain [12], and Pták [16]). However, it is still the case that very little is known concerning full-completeness in function spaces except when implied by formally stronger properties (e.g., Fréchet), and our aim in this article is to shed some light in this direction. Our approach is to use the unifying notion of the weighted spaces CV0(X) discussed in [19; 20], since such spaces provide a general setting for the study of virtually all continuous function spaces encountered in analysis.

The results to be presented here divide naturally into three sections with § 2 being consigned the preliminary definitions and theorems. In § 3 we obtain a necessary condition for full-completeness in a class of function spaces, and consider certain consequences of this result.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 22 , Issue 6 , 01 December 1970 , pp. 1196 - 1207
Copyright
Copyright © Canadian Mathematical Society 1970

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