Characterizations of Series in Banach Spaces
نویسنده
چکیده
In this paper we prove several new characterizations of weakly unconditionally Cauchy series in Banach spaces and in the dual space of a normed space. For a given series ζ, we consider the spaces S(ζ), Sw(ζ) and S0(ζ) of bounded sequences of real numbers (ai)i such that the series P i aixi is convergent, weakly convergent or ∗-weakly convergent, respectively. By means of these spaces we characterize conditionally and weakly unconditionally Cauchy series.
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