| 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:
|
2020-07-03 |
| 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 |
| . |
