Displaying 1081 – 1100 of 1168

Showing per page

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.

When does the Katětov order imply that one ideal extends the other?

Paweł Barbarski, Rafał Filipów, Nikodem Mrożek, Piotr Szuca (2013)

Colloquium Mathematicae

We consider the Katětov order between ideals of subsets of natural numbers (" K ") and its stronger variant-containing an isomorphic ideal ("⊑ "). In particular, we are interested in ideals for which K 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).

Currently displaying 1081 – 1100 of 1168