On a characterization of convergence in Banach spaces with a Schauder basis (Q2238433)

Summary: We extend the well-known characterizations of convergence in the spaces \(l_p\) (\(1\leq p<\infty\)) of \(p\)-summable sequences and \(c_0\) of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space \(c\) of convergent sequences.