Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...
Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...
Rearrangement of series. The theorem of Levy-Steiniz. - José Bonet ...
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<strong>The</strong> <strong>The</strong>orem <strong>Levy</strong> Steinitz.<br />
Idea <strong>of</strong> the pro<strong>of</strong> <strong>of</strong> the other inclusion: Continued:<br />
(C)<br />
∞�<br />
uk + ∩ ∞ ∞�<br />
m=1Zm ⊂ uk + ∩ ∞ m=1co(Zm).<br />
co(C) is the convex hull <strong>of</strong> C.<br />
(D)<br />
1<br />
1<br />
∞�<br />
uk + ∩ ∞ ∞�<br />
m=1co(Zm) = uk + Γ( � uk) ⊥ ,<br />
by the Hahn-Banach <strong>theorem</strong>.<br />
<strong>The</strong> problem is to find conditions to ensure that the inclusions (A) y (C)<br />
are equalities.<br />
1<br />
1<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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