Summable families in nuclear groups

• Autorzy: Wojciech Banaszczyk
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

nuclear groups; unconditional and absolute convergence

Kategorie tematyczne

• 22A10: Analysis on general topological groups
• 40J05: Summability in abstract structures (should also be assigned at least one other classification number in this section)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1993
• Tom: 105
• Numer: 3
• Strony: 271-282

Daty

wydano

1993

otrzymano

1992-11-03

poprawiono

1993-02-23

Twórcy

autor

Wojciech Banaszczyk

• Institute of Mathematics, Łódź University, 90-238 Łódź, Poland

Bibliografia

• [1] W. Banaszczyk, Additive Subgroups of Topological Vector Spaces, Lecture Notes in Math. 1466, Springer, Berlin 1991.
• [2] N. Bourbaki, Topologie générale, Chap. III, Groupes topologiques (Théorie élémentaire), Hermann, Paris 1960.
• [3] N. Kalton, Subseries convergence in topological groups and vector spaces, Israel J. Math. 10 (1971), 402-412.
• [4] A. Pietsch, Nuclear Locally Convex Spaces, Springer, Berlin 1972.