Turkish Journal of Mathematics
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.
Keywords
Schur property, Banach spaces. AMS Subject Classification: 46 B 20.
First Page
349
Last Page
354
Recommended Citation
TANBAY, BETÜL (1998) "Direct Sums and the Schur Property," Turkish Journal of Mathematics: Vol. 22: No. 3, Article 9. Available at: https://journals.tubitak.gov.tr/math/vol22/iss3/9
