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 ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
<strong>The</strong> <strong>The</strong>orem <strong>Levy</strong> Steinitz.<br />
<strong>The</strong> <strong>The</strong>orem <strong>Levy</strong> Steinitz. 1905, 1913.<br />
If � uk is a convergent <strong>series</strong> <strong>of</strong> vectors in R n , then<br />
S( � uk) =<br />
is an affine subspace <strong>of</strong> R n .<br />
∞�<br />
uk + Γ( � uk) ⊥<br />
1<br />
P. Rosenthal, in an article in the American Mathematical Monthly in<br />
1987 explaining this <strong>theorem</strong>, remarked that it is a beautiful result, which<br />
deserves to be better known, but that the difficulty <strong>of</strong> its pro<strong>of</strong> is out <strong>of</strong><br />
proportion <strong>of</strong> the statement.<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>.
Change language