Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-01-08T08:58:07.895Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

[1]Adasch, N., Ernst, B. and Keim, D., Topologioal vector spaces (Springer-Verlag, Berlin, Heidelberg, New York, 1978).Google Scholar
[2]Gulick, D., “Duality theory for the topology of simple convergence”, J. Math. Pures Appl. 52 (1973), 453–472.Google Scholar
[3]Hórvath, J., Topological vector spaces and distributions, Vol. 1 (Addison-Wesley, Reading, Massachusetts, 1966).Google Scholar
[4]Husain, T., “Two new classes of locally convex spaces”, Math. Ann. 166 (1966), 289–299.Google Scholar
[5]Kamthan, P.K. and Gupta, M., Sequences spaces and series (Lecture Notes 65. Marcel Dekker, New York, 1981).Google Scholar
[6]Köthe, G., Topological vector spaces 1 (translated by Garling, D.J.. Die Grundlehren der mathematischen Wissenschaften, 159. Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[7]McKennon, K. and Robertson, J.M., Locally convex spaces (Marcel Dekker, New York and Basel, 1976).Google Scholar