Abstract
1. Introduction. Let X be a Banach space (B-space). A sequence {s(i)} in X is unconditionally summable if and only if every rearrangement of the series Σis(i) is convergent. The set of unconditionally summable sequences in X will be written as U(X). In this paper several classes of summable sequences in X will be compared with one another. Each class to be considered is identical with U(X) when X has finite dimension.
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