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International Journal of Mathematics and Mathematical Sciences
Volume 30, Issue 8, Pages 449-457
http://dx.doi.org/10.1155/S0161171202011857

On weighted spaces without a fundamental sequence of bounded sets

Mathematics Department, University of Lagos, Yaba, Lagos, Nigeria

Received 5 February 2001; Revised 21 September 2001

Copyright © 2002 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

The problem of countably quasi-barrelledness of weighted spaces of continuous functions, of which there are no results in the general setting of weighted spaces, is tackled in this paper. This leads to the study of quasi-barrelledness of weighted spaces in which, unlike that of Ernst and Schnettler (1986), though with a similar approach, we drop the assumption that the weighted space has a fundamental sequence of bounded sets. The study of countably quasi-barrelledness of weighted spaces naturally leads to definite results on the weighted (DF)-spaces for those weighted spaces with a fundamental sequence of bounded sets.