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The Set of all Generalized Limits of Bounded Sequences

Published online by Cambridge University Press:  20 November 2018

Meyer Jerison
Meyer Jerison*
Affiliation:
Purdue University
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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

.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 79 - 89
Copyright
Copyright © Canadian Mathematical Society 1957

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