Closed subgroups in Banach spaces

Fredric Ancel; Tadeusz Dobrowolski; Janusz Grabowski

Studia Mathematica (1994)

  • Volume: 109, Issue: 3, page 277-290
  • ISSN: 0039-3223

Abstract

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We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of c 0 . Other results on subgroups of linear spaces are obtained.

How to cite

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Ancel, Fredric, Dobrowolski, Tadeusz, and Grabowski, Janusz. "Closed subgroups in Banach spaces." Studia Mathematica 109.3 (1994): 277-290. <http://eudml.org/doc/216074>.

@article{Ancel1994,
abstract = {We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of $c_0$. Other results on subgroups of linear spaces are obtained.},
author = {Ancel, Fredric, Dobrowolski, Tadeusz, Grabowski, Janusz},
journal = {Studia Mathematica},
keywords = {additive subgroup of linear space; basic sequence; weakly closed; topological dimension; zero-dimensional nondiscrete closed subgroups do exist in Banach spaces; subgroups of linear spaces},
language = {eng},
number = {3},
pages = {277-290},
title = {Closed subgroups in Banach spaces},
url = {http://eudml.org/doc/216074},
volume = {109},
year = {1994},
}

TY - JOUR
AU - Ancel, Fredric
AU - Dobrowolski, Tadeusz
AU - Grabowski, Janusz
TI - Closed subgroups in Banach spaces
JO - Studia Mathematica
PY - 1994
VL - 109
IS - 3
SP - 277
EP - 290
AB - We show that zero-dimensional nondiscrete closed subgroups do exist in Banach spaces E. This happens exactly when E contains an isomorphic copy of $c_0$. Other results on subgroups of linear spaces are obtained.
LA - eng
KW - additive subgroup of linear space; basic sequence; weakly closed; topological dimension; zero-dimensional nondiscrete closed subgroups do exist in Banach spaces; subgroups of linear spaces
UR - http://eudml.org/doc/216074
ER -

References

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