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A non-absolutely summing operator

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

I. J. Maddox  and
J. F. Price
I. J. Maddox
Affiliation:
Department of Pure Mathematics, Queen's University of Belfast, Belfast BT7 1NN, Northern Ireland
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Abstract

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In the case when 0 < p < 1 it is proved, using a method of Macphail that the identity map i: lp → lp is not (r, s)-absolutely summing for any r, s.

MSC classification

Secondary: 46A45: Sequence spaces (including Köthe sequence spaces)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 43 , Issue 1 , August 1987 , pp. 70 - 73
Copyright
Copyright © Australian Mathematical Society 1987

References

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Mitiagin, B. S. and Petczyński, A. (1966), ‘Nuclear operators and approximate dimension’, Proc. Int. Cong. Math., Moscow.Google Scholar
Orlicz, W. (1933), ‘Über unbedingte Konvergenz in Functionenraumen, II’, Studia Math. 4, 41–47.CrossRefGoogle Scholar