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Errata and addendum: tensor products and Dunford–Pettis sets

Published online by Cambridge University Press:  01 September 2007

Ioana Ghenciu  and
Paul Lewis
Ioana Ghenciu
Affiliation:
Department of Mathematics, University of Wisconsin at River Falls, River Falls, Wisconsin 54022-5001, U.S.A. email: ioana.ghenciu@uwrf.edu
Paul Lewis
Affiliation:
University of North Texas, Department of Mathematics, Box 311430, Denton, Texas 76203-1430, U.S.A. email: lewis@unt.edu
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Abstract

Ghenciu and Lewis introduced the notion of a strong Dunford–Pettis set and used this notion to study the presence or absence of isomorphic copies of c0 in Banach spaces. The authors asserted that they could obtain a fundamental result of J. Elton without resorting to Ramsey theory. While the stated theorems are correct, unfortunately there is a flaw in the proof of the first theorem in the paper which also affects subsequent corollaries and theorems. The difficulty is discussed, and Elton's results are employed to establish a Schauder basis proposition which leads to a quick proof of the theorem in question. Additional results where questions arise are discussed on an individual basis.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 387 - 390
Copyright
Copyright © Cambridge Philosophical Society 2007

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References

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