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On Isomorphisms of Locally Convex Spaces With Similar Biorthogonal Systems

Published online by Cambridge University Press:  20 November 2018

F. Bozel  and
T. Husain
F. Bozel
Affiliation:
Mcmaster University, Hamilton Ontario
T. Husain
Affiliation:
Mcmaster University, Hamilton Ontario
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The relationship between bases and isomorphisms (i.e. linear homeomorphisms) between complete metrizable linear spaces has been studied with great interest by Arsove and Edwards (see [1] and [2]). We prove (Theorem 1) that in the case of B-complete barrelled spaces, similar generalized bases imply existence of an isomorphism. This result was also proved by Dyer and Johnson [4], so we do not give a proof. We show (Theorem 6) that if one assumes that the bases are Schauder and similar, then Theorem 1 holds for countably barrelled spaces. We use Theorem 1 to advantage (Theorems 2-5) to show that one can improve some results due to Davis [3].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 179 - 183
Copyright
Copyright © Canadian Mathematical Society 1973

References

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