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On two new classes of locally convex spaces

Published online by Cambridge University Press:  17 April 2009

Kazuaki Kitahara
Kazuaki Kitahara
Affiliation:
Department of Mathematics, Kobe University, Nada-ku, Kobe 657, Japan.
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Abstract

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The purpose of this paper is to introduce two new classes of locally convex spaces which contain the classes of semi-Montel and Montel spaces. Further we give some examples and study some properties of these classes. As to permanence properties, these classes have similar properties to semi-Montel and Montel spaces except strict inductive limits and these classes are not always preserved under their completions. We shall call these two classes as β–semi–Montel and β–Montel spaces. A β–semi–Montel space is obtained by replacing the word “bounded” by “strongly bounded” in the definition of a semi–Montel space. If a β–semi–Montel space is infra-barrelled, we call the space β–Montel.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 3 , December 1983 , pp. 383 - 392
Copyright
Copyright © Australian Mathematical Society 1983

References

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