Tao, Yuanhong; Li, Ronglu; Cui, Chengri The uniform forward sets of \(C(X)\) and uniform convergence of operator series. (English) Zbl 1145.46004 Taiwanese J. Math. 11, No. 4, 1113-1118 (2007). Summary: We introduce the uniform forward sets of \(C(X)\), the space of \(X\)-valued convergent sequences, and show that each totally bounded set of \(C(X)\) is a uniform forward set, moreover, we prove that the uniform forward sets of \(C(X)\) are just the largest subset family of \(C(X)\) on which each \(C(X)\)-evaluation convergent operator series is uniformly convergent. Cited in 1 Document MSC: 46A45 Sequence spaces (including Köthe sequence spaces) 46B99 Normed linear spaces and Banach spaces; Banach lattices PDFBibTeX XMLCite \textit{Y. Tao} et al., Taiwanese J. Math. 11, No. 4, 1113--1118 (2007; Zbl 1145.46004) Full Text: DOI