Direct Sums and the Schur Property
Authors : Betül Tanbay
Pages : 349-354
View : 10 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :It is a known fact that \ell1, the dual space of the null sequences c0, has the Schur property, that is, weakly convergent sequences in \ell1 are norm convergent. In this paper, we prove that if (Xa)a\in I are Banach spaces and X=(\oplusa\in IXa)1 their l1-sum, then the space X has the Schur property iff each factor Xa has it.Keywords : Schur property, Banach spaces. AMS Subject Classification: 46 B 20.