# Article

 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: http://hdl.handle.net/10338.dmlcz/127614 . 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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