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  • 1 Harbin Institute of Technology Department of Mathematics 150001 Harbin China
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Suppose X is a locally convex space, Y is a topological vector space and λ(X)βY is the β-dual of some X valued sequence space λ(X). When λ(X) is c0(X) or l(X), we have found the largest M ⊂ 2λ(X) for which (Aj) ∈ λ(X)βY if and only if Σ j=1Aj(xj) converges uniformly with respect to (xj) in any MM. Also, a remark is given when λ(X) is lp(X) for 0 < p < + ∞.

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