A short proof of Pitt’s compactness theorem
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- Proc. Amer. Math. Soc. 137 (2009), 1371-1372 Request permission
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 $1\leq q<p<\infty$.References
- Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalucía, Jan Pelant, and Václav Zizler, Functional analysis and infinite-dimensional geometry, CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, vol. 8, Springer-Verlag, New York, 2001. MR 1831176, DOI 10.1007/978-1-4757-3480-5
- M. Fabian and V. Zizler, A “nonlinear” proof of Pitt’s compactness theorem, Proc. Amer. Math. Soc. 131 (2003), no. 12, 3693–3694. MR 1998188, DOI 10.1090/S0002-9939-03-07200-9
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
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1371-1372
- MSC (2000): Primary 46B25
- DOI: https://doi.org/10.1090/S0002-9939-08-09617-2
- MathSciNet review: 2465661