Errata and addendum: tensor products and Dunford¿Pettis sets

• Autores: Ioana Ghenciu, Paul W. Lewis
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 143, Nº 2, 2007, págs. 387-390
• Idioma: inglés
• DOI: 10.1017/s0305004107000102
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• Resumen

  • 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