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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Weakly compact operators into sequence spaces: A counterexample


Author: Kari Ylinen
Journal: Proc. Amer. Math. Soc. 133 (2005), 1423-1425
MSC (2000): Primary 46B45
Published electronically: November 19, 2004
Erratum: Proc. Amer. Math. Soc. 134 (2006), 311-311.
MathSciNet review: 2111968
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Abstract: In a recent paper Gutiérrez and Villanueva have used, without giving a detailed proof, an analogue of a well-known result of Ryan characterizing the weakly compact operators from a Banach space $E$ into the space $c_0(X)$ of null sequences in a Banach space $X$. In this note a counterexample is given showing that in the statement of Gutiérrez and Villanueva an additional condition is needed.


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Additional Information

Kari Ylinen
Affiliation: Department of Mathematics, University of Turku, FIN-20014 Turku, Finland
Email: ylinen@utu.fi

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07771-8
PII: S 0002-9939(04)07771-8
Keywords: Weakly compact operator, Banach sequence space, Yosida-Hewitt decomposition
Received by editor(s): January 8, 2004
Published electronically: November 19, 2004
Communicated by: N.Tomczak-Jaegermann
Article copyright: © Copyright 2004 American Mathematical Society