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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
MathSciNet review:
2465661
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Abstract |
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Abstract:
We give a short proof of Pitt's theorem that every bounded linear operator from  or  into  is compact whenever  .
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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