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Closed subgroups in Banach spaces

100%

D. Ancel F., Dobrowolski T., Grabowski J.

Studia Mathematica

1994

tom 109

nr 3

277-290

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.

Topological type of weakly closed subgroups in Banach spaces

88%

Dobrowolski T., Grabowski J., Kawamura K.

Studia Mathematica

1996

tom 118

nr 1

49-62

The main result says that nondiscrete, weakly closed, containing no nontrivial linear subspaces, additive subgroups in separable reflexive Banach spaces are homeomorphic to the complete Erdős space. Two examples of such subgroups in $ℓ^1$ which are interesting from the Banach space theory point of view are discussed.

Ograniczanie wyników

2 Studia Mathematica

2 Dobrowolski T.

2 Grabowski J.

1 D. Ancel F.

1 Kawamura K.

1 1996

1 1994

Wyniki wyszukiwania

Closed subgroups in Banach spaces

Topological type of weakly closed subgroups in Banach spaces