Uebr die Convergenz einer aus Primzahlpotenzen gebildeten unendlichen Reihe
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series in a topological vector space X is called ℒ-convergent if each of its lacunary subseries (i.e. those with ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence...
In this paper, a vector topology is introduced in the vector-valued sequence space and convergence of sequences and sequentially compact sets in are characterized.
We consider the Katětov order between ideals of subsets of natural numbers ("") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which for every ideal . We find examples of ideals with this property and show how this property can be used to reformulate some problems known from the literature in terms of the Katětov order instead of the order "⊑ " (and vice versa).