| Title:
|
Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series (English) |
| Author:
|
Pérez-Fernández, F. J. |
| Author:
|
Benítez-Trujillo, F. |
| Author:
|
Aizpuru, A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
50 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
889-896 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space $X$ can be characterized through the behaviour of its weakly-$\ast $ unconditionally Cauchy series in $X^\ast $. (English) |
| Keyword:
|
completeness |
| Keyword:
|
barrelledness |
| Keyword:
|
weakly unconditionally Cauchy series |
| MSC:
|
40A05 |
| MSC:
|
46B15 |
| MSC:
|
46B45 |
| idZBL:
|
Zbl 1079.46505 |
| idMR:
|
MR1792978 |
| . |
| Date available:
|
2009-09-24T10:38:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127618 |
| . |
| Reference:
|
[aizp] A. Aizpuru and F. J. Pérez-Fernández: Spaces of $\mathcal{S}$-bounded multiplier convergent series.Acta Math. Hungar. 87 (2000), 103–114. MR 1755883, 10.1023/A:1006781218759 |
| Reference:
|
[BP58a] C. Bessaga and A. Pelczynski: On bases and unconditional convergence of series in Banach spaces.Stud. Math. 17 (1958), 151–164. MR 0115069, 10.4064/sm-17-2-151-164 |
| Reference:
|
[Diestel] J. Diestel: Sequences and Series in Banach Spaces.Springer-Verlag, New York, 1984. MR 0737004 |
| Reference:
|
[Kadets91] V. M. Kadets and M. I. Kadets: Rearrangements of Series in Banach Spaces. Translations of Mathematical Monographs. 86.Amer. Math. Soc., Providence, 1991. MR 1108619, 10.1090/mmono/086 |
| Reference:
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[Mc56] C. W. McArthur: On relationships amongst certain spaces of sequences in an arbitrary Banach space.Canad. J. Math. 8 (1956), 192–197. Zbl 0074.32305, MR 0078662, 10.4153/CJM-1956-022-0 |
| Reference:
|
[Qingying] Q. Bu and C. Wu: Unconditionally convergent series of operators on Banach spaces.J. Math. Anal. Appl. 207 (1997), 291–299. MR 1438915, 10.1006/jmaa.1997.5218 |
| Reference:
|
[Li] R. Li and Q. Bu: Locally convex spaces containing no copy of $c_0$.J. Math. Anal. Appl. 172 (1993), 205–211. MR 1199505, 10.1006/jmaa.1993.1017 |
| . |
