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On the Weak Basis Theorem in F-spaces

Published online by Cambridge University Press:  20 November 2018

Joel H. Shapiro
Joel H. Shapiro*
Affiliation:
Michigan State University, East Lansing, Michigan
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It is well-known that every weak basis in a Fréchet space is actually a basis. This result, called the weak basis theorem was first given for Banach spaces in 1932 by Banach [1, p. 238], and extended to Fréchet spaces by Bessaga and Petczynski [3]. McArthur [12] proved an analogue for bases of subspaces in Fréchet spaces, and recently W. J. Stiles [18, Corollary 4.5, p. 413] showed that the theorem fails in the non-locally convex spaces lp (0 < p < 1). The purpose of this paper is to prove the following generalization of Stiles' result.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1294 - 1300
Copyright
Copyright © Canadian Mathematical Society 1974

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