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A short proof of Pitt's compactness theorem

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

References:

1.: M. Fabian, P. Habala, P. Hájek, V. Montesinos Santalucía, J. Pelant and V. Zizler, Functional analysis and infinite-dimensional geometry, CMS Books in Mathematics, Springer-Verlag, New York, 2001. MR 1831176 (2002f:46001)
2.: M. Fabian and V. Zizler, A ``nonlinear" proof of Pitt's compactness theorem, Proc. Amer. Math. Soc. 131 (2003), 3693-3694. MR 1998188 (2004g:46026)

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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: 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
Posted: October 17, 2008
Communicated by: Nigel J. Kalton
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.


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