Continuity Theory by Louis Nel

Author:Louis Nel
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

X6.4H Absolutely Summable Families

Let E be a Banach space, D a denumerable set. Call an absolutely summable family if for some bijection the series with general term x b(n) is absolutely convergent. (a)Show that is absolutely summable iff the set of finite sums with J a finite subset of D is a bounded set.

(b)Let be absolutely summable. Show that for any there exists a finite subset such that for every finite subset we have and .

6.5 CV-Spaces and CV-Mappings

6.5.1 Convergence Vector Spaces

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