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On Relationships Amongst Certain Spaces Of Sequences In An Arbitrary Banach Space

Published online by Cambridge University Press:  20 November 2018

C. W. McArthur
C. W. McArthur*
Affiliation:
Alabama Polytechnic Institute
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1. Introduction. Let X be a Banach space (B-space). A sequence {s(i)} in X is unconditionally summable if and only if every rearrangement of the series Σis(i) is convergent. The set of unconditionally summable sequences in X will be written as U(X). In this paper several classes of summable sequences in X will be compared with one another. Each class to be considered is identical with U(X) when X has finite dimension.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 8 , 1956 , pp. 192 - 197
Copyright
Copyright © Canadian Mathematical Society 1956

References

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