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Series in locally convex spaces and inclusions between FK spaces

Published online by Cambridge University Press:  24 October 2008

I. J. Maddox
I. J. Maddox
Affiliation:
The Queen's University of Belfast
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Extract

Singer [10] defined a series Σxk in a Banach space X to be weakly p-unconditionally Cauchy if and only if Σλkxk converges in X for all λ∊lp, where 1 < p < ∞. For Banach spaces containing no subspace isomorphic to c0 Singer characterized such series as those for which

where 1/p + 1/q = 1 and X′ is the dual space of X.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 95 , Issue 3 , May 1984 , pp. 467 - 472
Copyright
Copyright © Cambridge Philosophical Society 1984

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References

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