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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  8. [DG] T. Dobrowolski and J. Grabowski, Subgroups of Hilbert spaces, Math. Z. 211 (1992), 657-669. 
  9. [DT] T. Dobrowolski and H. Toruńczyk, Separable complete ANR's admitting a group structure are Hilbert manifolds, Topology Appl. 12 (1981), 229-235. Zbl0472.57009
  10. [E] R. Engelking, Dimension Theory, North-Holland, Amsterdam, 1978. 
  11. [K] N. J. Kalton, Basic sequences in F-spaces and their applications, Proc. Edinburgh Math. Soc. 19 (1974), 151-177. Zbl0296.46010
  12. [P] A. Pełczyński, Projections in certain Banach spaces, Studia Math. 19 (1960), 209-228. Zbl0104.08503
  13. [T] H. Toruńczyk, Characterizing Hilbert space topology, Fund. Math. 111 (1981), 247-262. Zbl0468.57015

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