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

 

A short proof of Pitt's compactness theorem


Author: Sylvain Delpech
Journal: Proc. Amer. Math. Soc. 137 (2009), 1371-1372
MSC (2000): Primary 46B25
Published electronically: October 17, 2008
MathSciNet review: 2465661
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Abstract: We give a short proof of Pitt's theorem that every bounded linear operator from $ \ell_p$ or $ c_0$ into $ \ell_q$ is compact whenever $ 1\leq q<p<\infty$.


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Additional Information

Sylvain Delpech
Affiliation: Institut de Mathématiques de Bordeaux, UMR 5251, Université Bordeaux I, 351, Cours de la Libération, 33405 Talence Cedex, France
Email: sylvain.delpech@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09617-2
PII: S 0002-9939(08)09617-2
Keywords: $\ell _p$ space, $c_0$ space, compact operator.
Received by editor(s): February 6, 2008
Received by editor(s) in revised form: April 16, 2008
Published electronically: October 17, 2008
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.