The Set of all Generalized Limits of Bounded Sequences
- 1 January 1957
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 9, 79-89
- https://doi.org/10.4153/cjm-1957-012-x
Abstract
Let M be the normed linear space whose general element, x, is a bounded sequence of real numbers, and ‖x‖ = l.u.b. |ξn|. Let T denote the linear operation (of norm 1) defined by Tx = (ξ2, ξ3, … , ξn+1,…). A generalized limit is a linear functional ϕ on M which satisfies the conditions .Keywords
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