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The Unrestricted Section Properties of Sequences

Published online by Cambridge University Press:  20 November 2018

John Sember  and
Marc Raphael
John Sember
Affiliation:
Simon Fraser University, Burnaby, British Columbia
Marc Raphael
Affiliation:
Simon Fraser University, Burnaby, British Columbia
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1. Introduction. An unrestricted section of a sequence x is any sequence of the form Σk∈Fxkδk, where F is some finite subset of the natural numbers. The notion of boundedness of the set of unrestricted sections of a sequence in a K-space was studied in [10], and called unconditional section boundedness (UAB). It was shown in [10] (Theorem 7) that the class of FK-spaces in which every element has UAB consists of those FK-spaces that are invariant under coordinatewise multiplication by the convergent sequences.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 331 - 336
Copyright
Copyright © Canadian Mathematical Society 1979

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