On p - Summable Sequences in Locally Convex Spaces †
نویسندگان
چکیده
We follow the notation of [7,10]. In particular, if E[τ ] is a locally convex space (in short l.c.s.), σ(E, E∗), μ(E,E∗) and β(E,E∗) will denote, respectively, the weak, Mackey and strong topology corresponding to the dual pair 〈E, E∗〉. If U is a neighbourhood of 0 in E[τ ], EU denotes the Banach space associated to U and φU : E → EU denotes the corresponding quotient map. Definition 1. Let E[τ ] be an l.c.s. and let 1 ≤ p < +∞. A sequence (xn) in E is said to be p-summable if, for each τ -continuous seminorm q, ∑ n q(xn) p < +∞.
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