Unconditional convergence and the Vitali-Hahn-Saks theorem

Alex.P. Robertson

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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 $\sum_{n} x_{n}$ in a topological vector space X is called ℒ-convergent if each of its lacunary subseries $\sum_{k} x_{n_{k}}$ (i.e. those with $n_{k + 1} - n_{k} \to \infty$ ) 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...

Displaying similar documents to “Unconditional convergence and the Vitali-Hahn-Saks theorem”

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