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Vector series whose lacunary subseries converge

Lech Drewnowski, Iwo Labuda (2000)

Studia Mathematica

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 n x n in a topological vector space X is called ℒ-convergent if each of its lacunary subseries k x n k (i.e. those with n k + 1 - n k ) 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...

Vector-valued sequence space B M C ( X ) and its properties

Qing-Ying Bu (1996)

Commentationes Mathematicae Universitatis Carolinae

In this paper, a vector topology is introduced in the vector-valued sequence space BMC ( X ) and convergence of sequences and sequentially compact sets in BMC ( X ) are characterized.

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