Sequential retractivities and regularity on inductive limits
Czechoslovak Mathematical Journal (2000)
- Volume: 50, Issue: 4, page 847-851
- ISSN: 0011-4642
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topJing-Hui, Qiu. "Sequential retractivities and regularity on inductive limits." Czechoslovak Mathematical Journal 50.4 (2000): 847-851. <http://eudml.org/doc/30604>.
@article{Jing2000,
abstract = {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.},
author = {Jing-Hui, Qiu},
journal = {Czechoslovak Mathematical Journal},
keywords = {inductive limits; regularity; sequential retractivities; inductive limits; regularity; sequential retractivities},
language = {eng},
number = {4},
pages = {847-851},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Sequential retractivities and regularity on inductive limits},
url = {http://eudml.org/doc/30604},
volume = {50},
year = {2000},
}
TY - JOUR
AU - Jing-Hui, Qiu
TI - Sequential retractivities and regularity on inductive limits
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 847
EP - 851
AB - 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.
LA - eng
KW - inductive limits; regularity; sequential retractivities; inductive limits; regularity; sequential retractivities
UR - http://eudml.org/doc/30604
ER -
References
top- An introduction to locally convex inductive limit, In: Functional Analysis and its Applications, Singapore-New Jersey-Hong Kong, 1988, pp. 35–133. (1988) MR0979516
- Folgenretraktive Sequenzen lokalkonvexer Räume, J. Reine Angew. Math. 259 (1973), 65–85. (1973) Zbl0251.46003MR0313748
- 10.1007/BF01197594, Arch. Math. 67 (1996), 302–307. (1996) Zbl0858.46007MR1407333DOI10.1007/BF01197594
- Barrelled locally convex spaces, North-Holland Math. Stud. 131, Amsterdam, 1987. (1987) MR0880207
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