FULLY AND STRONGLY ALMOST SUMMING MULTILINEAR MAPPINGS

In this paper we generalize a theorem of Kwapień which asserts that a linear operator T is absolutely (1; 1)-summing whenever T* is absolutely (q; q)-summing for some q ≥ 1. We also introduce the classes of strongly and fully almost summing multilinear mappings and investigate structural properties...

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Bibliographic Details
Published in:The Rocky Mountain journal of mathematics 2006-01, Vol.36 (2), p.683-698
Main Authors: PELLEGRINO, DANIEL M., SOUZA, MARCELA L.V.
Format: Article
Language:English
Subjects:
46E50
46G20
Banach space
Coincidence
Hilbert spaces
Linear transformations
Mathematical theorems
Polynomials
Random variables
Scalars
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Summary:In this paper we generalize a theorem of Kwapień which asserts that a linear operator T is absolutely (1; 1)-summing whenever T* is absolutely (q; q)-summing for some q ≥ 1. We also introduce the classes of strongly and fully almost summing multilinear mappings and investigate structural properties such as a Dvoretzky-Rogers type theorem and connections with other classes of absolutely summing mappings.
ISSN:0035-7596
1945-3795
DOI:10.1216/rmjm/1181069474