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

 

The Schur property on projective and injective tensor products


Authors: Geraldo Botelho and Pilar Rueda
Journal: Proc. Amer. Math. Soc. 137 (2009), 219-225
MSC (2000): Primary 46G20; Secondary 46A04, 46A32
Published electronically: May 22, 2008
MathSciNet review: 2439444
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Abstract: The problem of whether the Schur property is passed from a Banach space to its (symmetric) projective $ n$-fold tensor product is reformulated in the language of polynomial ideals. As a result, a very closely related question is solved in the negative. It is also proved that the injective tensor product of infrabarrelled locally convex spaces with the Schur property has the Schur property as well.


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Additional Information

Geraldo Botelho
Affiliation: Faculdade de Matemática, Universidade Federal de Uberlândia, 38.400-902, Uberlândia, Brazil
Email: botelho@ufu.br

Pilar Rueda
Affiliation: Departamento de Análisis Matemático, Universidad de Valencia, 46.100 Burjasot, Valencia, Spain
Email: pilar.rueda@uv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09486-0
PII: S 0002-9939(08)09486-0
Received by editor(s): September 24, 2007
Received by editor(s) in revised form: December 27, 2007
Published electronically: May 22, 2008
Additional Notes: The first author was supported by CNPq Project 202162/2006-0
The second author was supported by MEC and FEDER Project MTM2005-08210
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.