Ueber die Multiplication bedingt convergenter Reihen
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.