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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

Bennett, G. (1973), ‘Inclusion mappings between lp spaces’, J. Functional Analysis 13, 20–27.CrossRefGoogle Scholar
Macphail, M. S. (1947), ‘Absolute and unconditional convergence’, Bull. Amer. Math. Soc. 53, 121–123.CrossRefGoogle Scholar
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