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Turkish Journal of Mathematics

Authors

BETÜL TANBAY

DOI

-

Abstract

It is a known fact that $\ell^1$, the dual space of the null sequences $c_0$, has the Schur property, that is, weakly convergent sequences in $\ell^1$ are norm convergent. In this paper, we prove that if $(X_{\alpha})_{\alpha\in I}$ are Banach spaces and $X=(\oplus_{\alpha\in I}X_{\alpha})_1$ their $l_1$-sum, then the space $X$ has the Schur property iff each factor $X_{\alpha}$ has it.

First Page

349

Last Page

354

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Mathematics Commons

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