We discuss some properties of the Banach-valued sequence space p[X] (1 ≤ p < ∞), the space of weakly p-summable sequences on a Banach space X. For example, we characterize the reflexivity of p[X], convergent sequences on p[X], and compact subsets of p[X]. 2000 Mathematics Subject Classification. 40A05, 46B45.
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