Unconditional Convergence in Banach Spaces
نویسنده
چکیده
Introduction. This note investigates an apparent generalization of unconditionally convergent series ^ x » in weakly complete Banach spaces. A series of elements with Xi in E is said to be unconditionally convergent if for every variation of sign €j= ± 1 , ^TMeiXi is convergent. This formulation of the definition of unconditional convergence is equivalent to that given by Orliczjé]. We call ^Xi unconditionally summable if there exists a finite row Toeplitz matrix (bik) such that for every variation of sign a \= ]C*-A*& 2?-i** converges. The fact that unconditional summability implies unconditional convergence is established in this note. Finally, applications to orthogonal functions are presented.
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