Displaying similar documents to “A few remarks on the results of Rosinski and Suchanecki concerning unconditional convergence and C -sequences”

Vector series whose lacunary subseries converge

Lech Drewnowski, Iwo Labuda (2000)

Studia Mathematica

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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...

Remarks on several types of convergence of bounded sequences

Vladimír Baláž, Oto Strauch, Tibor Šalát (2006)

Acta Mathematica Universitatis Ostraviensis

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In this paper we analyze relations among several types of convergences of bounded sequences, in particulars among statistical convergence, ℐ u -convergence, ϕ -convergence, almost convergence, strong p -Cesàro convergence and uniformly strong p -Cesàro convergence.