Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series

Francisco Javier Pérez Fernández; F. Benítez-Trujillo; Antonio Aizpuru Tomás

Czechoslovak Mathematical Journal (2000)

  • Volume: 50, Issue: 4, page 889-896
  • ISSN: 0011-4642

Abstract

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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- * unconditionally Cauchy series in X * .

How to cite

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Pérez Fernández, Francisco Javier, Benítez-Trujillo, F., and Aizpuru Tomás, Antonio. "Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series." Czechoslovak Mathematical Journal 50.4 (2000): 889-896. <http://eudml.org/doc/30608>.

@article{PérezFernández2000,
abstract = {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 $.},
author = {Pérez Fernández, Francisco Javier, Benítez-Trujillo, F., Aizpuru Tomás, Antonio},
journal = {Czechoslovak Mathematical Journal},
keywords = {completeness; barrelledness; weakly unconditionally Cauchy series; completeness; barrelledness; weakly unconditionally Cauchy series},
language = {eng},
number = {4},
pages = {889-896},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series},
url = {http://eudml.org/doc/30608},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Pérez Fernández, Francisco Javier
AU - Benítez-Trujillo, F.
AU - Aizpuru Tomás, Antonio
TI - Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series
JO - Czechoslovak Mathematical Journal
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 889
EP - 896
AB - 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 $.
LA - eng
KW - completeness; barrelledness; weakly unconditionally Cauchy series; completeness; barrelledness; weakly unconditionally Cauchy series
UR - http://eudml.org/doc/30608
ER -

References

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  1. 10.1023/A:1006781218759, Acta Math. Hungar. 87 (2000), 103–114. (2000) MR1755883DOI10.1023/A:1006781218759
  2. 10.4064/sm-17-2-151-164, Stud. Math. 17 (1958), 151–164. (1958) MR0115069DOI10.4064/sm-17-2-151-164
  3. Sequences and Series in Banach Spaces, Springer-Verlag, New York, 1984. (1984) MR0737004
  4. 10.1090/mmono/086, Amer. Math. Soc., Providence, 1991. (1991) MR1108619DOI10.1090/mmono/086
  5. 10.4153/CJM-1956-022-0, Canad. J. Math. 8 (1956), 192–197. (1956) Zbl0074.32305MR0078662DOI10.4153/CJM-1956-022-0
  6. 10.1006/jmaa.1997.5218, J. Math. Anal. Appl. 207 (1997), 291–299. (1997) MR1438915DOI10.1006/jmaa.1997.5218
  7. 10.1006/jmaa.1993.1017, J. Math. Anal. Appl. 172 (1993), 205–211. (1993) MR1199505DOI10.1006/jmaa.1993.1017

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