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Title: Sequential retractivities and regularity on inductive limits (English)
Author: Jing-Hui, Qiu
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 50
Issue: 4
Year: 2000
Pages: 847-851
Summary lang: English
Category: math
Summary: In this paper we prove the following result: an inductive limit $(E,t) = \text{ind}(E_n,t_n)$ is regular if and only if for each Mackey null sequence $(x_k)$ in $(E,t)$ there exists $n=n(x_k)\in \mathbb N$ such that $(x_k)$ is contained and bounded in $(E_n,t_n)$. From this we obtain a number of equivalent descriptions of regularity. (English)
Keyword: inductive limits
Keyword: regularity
Keyword: sequential retractivities
MSC: 46A13
MSC: 46M40
idZBL: Zbl 1079.46501
idMR: MR1792974
Date available: 2009-09-24T10:38:25Z
Last updated: 2016-04-07
Stable URL:
Reference: [1] K. D. Bierstedt: An introduction to locally convex inductive limit.In: Functional Analysis and its Applications, Singapore-New Jersey-Hong Kong, 1988, pp. 35–133. MR 0979516
Reference: [2] K. Floret: Folgenretraktive Sequenzen lokalkonvexer Räume.J. Reine Angew. Math. 259 (1973), 65–85. Zbl 0251.46003, MR 0313748
Reference: [3] Q. Jing-Hui: Retakh’s conditions and regularity properties of (LF)-spaces.Arch. Math. 67 (1996), 302–307. Zbl 0858.46007, MR 1407333, 10.1007/BF01197594
Reference: [4] J. Bonet and P. Perez Carreras: Barrelled locally convex spaces.North-Holland Math. Stud. 131, Amsterdam, 1987. MR 0880207


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