Turkish Journal of Mathematics
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.
DOI
-
Keywords
Schur property, Banach spaces. AMS Subject Classification: 46 B 20.
First Page
349
Last Page
354
Recommended Citation
TANBAY, B (1998). Direct Sums and the Schur Property. Turkish Journal of Mathematics 22 (3): 349-354. https://doi.org/-
