On the Group of Absolutely Summable Sequences
Copyright policy ) Lydia Außenhofer;
On the Group of Absolutely Summable Sequences
For an abelian topological group G, the sequence group ℓ1(G) of all absolutely summable sequences in G is studied. It is shown that ℓ1(G) is a Pontryagin reflexive group in case G is a reflexive metrizable group or an LCA group. Further, ℓ1(G) has the Schur property if and only if G has it and ℓ1(G) is a Schwartz group if and only if G is linearly topologized.
- University of Passau Germany
LCA groups, nuclear group, summable sequence, Schwartz group, locally quasi-convex group, Pontryagin reflexive group, QA1-939, absolutely summable sequence, Mathematics, Schur property
LCA groups, nuclear group, summable sequence, Schwartz group, locally quasi-convex group, Pontryagin reflexive group, QA1-939, absolutely summable sequence, Mathematics, Schur property
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