Geodesic
Sequential retractivities and regularity on inductive limits
Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 847-851 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 46A13, 46M40
Keywords: inductive limits; regularity; sequential retractivities 
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Jing-Hui, Qiu. Sequential retractivities and regularity on inductive limits. Czechoslovak Mathematical Journal, Tome 50 (2000) no. 4, pp. 847-851. http://geodesic.mathdoc.fr/item/CMJ_2000_50_4_a11/

[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

[2] K. Floret: Folgenretraktive Sequenzen lokalkonvexer Räume. J. Reine Angew. Math. 259 (1973), 65–85. | MR | Zbl

[3] Q. Jing-Hui: Retakh’s conditions and regularity properties of (LF)-spaces. Arch. Math. 67 (1996), 302–307. | DOI | MR | Zbl

[4] J. Bonet and P. Perez Carreras: Barrelled locally convex spaces. North-Holland Math. Stud. 131, Amsterdam, 1987. | MR