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Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...

Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...

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Other open problems.<br />

Does every non-nuclear Fréchet space contain a convergent <strong>series</strong><br />

� uk such that its set <strong>of</strong> sums consists exactly <strong>of</strong> two points?<br />

Improve the converse for non-metrizable spaces.<br />

Find concrete spaces E and conditions on a convergent <strong>series</strong> � uk<br />

in E to ensure that the set <strong>of</strong> sums S( � uk) has exactly the form <strong>of</strong><br />

the <strong>The</strong>orem <strong>of</strong> <strong>Levy</strong> and Steinitz. Chasco and Chobayan have<br />

results <strong>of</strong> this type for spaces Lp <strong>of</strong> p-integrable functions.<br />

<strong>José</strong> <strong>Bonet</strong> <strong>Rearrangement</strong> <strong>of</strong> <strong>series</strong>. <strong>The</strong> <strong>theorem</strong> <strong>of</strong> <strong>Levy</strong>-<strong>Steiniz</strong>.

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