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| UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES |
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Citation： |
A. AIZPURU,A. GUTIERREZ-DAVILA.UNCONDITIONAL CAUCHY SERIES AND UNIFORM CONVERGENCE ON MATRICES[J].Chinese Annals of Mathematics B,2004,25(3):335~346 |
| Page view： 1240
Net amount： 765 |
Authors： |
A. AIZPURU; A. GUTIERREZ-DAVILA |
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| Abstract： |
The authors obtain new characterizations of unconditional Cauchy
series in terms of separation properties of subfamilies of
$\mathcal{P}(\mathbb N)$, and a generalization of the
Orlicz-Pettis Theorem is also obtained. New results on the uniform
convergence on matrices and a new version of the Hahn-Schur
summation theorem are proved. For matrices whose rows define
unconditional Cauchy series, a better sufficient condition for the
basic Matrix Theorem of Antosik and Swartz, new necessary
conditions and a new proof of that theorem are given. |
Keywords： |
Unconditional Cauchy series, Orlicz-Pettis theorem, Summation, Hahn-
Schur theorem, Basic matrix theorem |
Classification： |
46B15, 46B25 |
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