Summable families in nuclear groups
Studia Mathematica (1993)
- Volume: 105, Issue: 3, page 271-282
- ISSN: 0039-3223
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topBanaszczyk, Wojciech. "Summable families in nuclear groups." Studia Mathematica 105.3 (1993): 271-282. <http://eudml.org/doc/215999>.
@article{Banaszczyk1993,
abstract = {Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.},
author = {Banaszczyk, Wojciech},
journal = {Studia Mathematica},
keywords = {nuclear groups; unconditional and absolute convergence; abelian topological groups; LCA groups; nuclear locally convex spaces; weakly summable families; strongly summable; absolutely summable},
language = {eng},
number = {3},
pages = {271-282},
title = {Summable families in nuclear groups},
url = {http://eudml.org/doc/215999},
volume = {105},
year = {1993},
}
TY - JOUR
AU - Banaszczyk, Wojciech
TI - Summable families in nuclear groups
JO - Studia Mathematica
PY - 1993
VL - 105
IS - 3
SP - 271
EP - 282
AB - Nuclear groups form a class of abelian topological groups which contains LCA groups and nuclear locally convex spaces, and is closed with respect to certain natural operations. In nuclear locally convex spaces, weakly summable families are strongly summable, and strongly summable are absolutely summable. It is shown that these theorems can be generalized in a natural way to nuclear groups.
LA - eng
KW - nuclear groups; unconditional and absolute convergence; abelian topological groups; LCA groups; nuclear locally convex spaces; weakly summable families; strongly summable; absolutely summable
UR - http://eudml.org/doc/215999
ER -
References
top- [1] W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Math. 1466, Springer, Berlin 1991. Zbl0743.46002
- [2] N. Bourbaki, Topologie générale, Chap. III, Groupes topologiques (Théorie élémentaire), Hermann, Paris 1960. Zbl0102.27104
- [3] N. Kalton, Subseries convergence in topological groups and vector spaces, Israel J. Math. 10 (1971), 402-412. Zbl0226.22005
- [4] A. Pietsch, Nuclear Locally Convex Spaces, Springer, Berlin 1972.
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