A “nonlinear” proof of Pitt’s compactness theorem
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- by M. Fabian and V. Zizler
- Proc. Amer. Math. Soc. 131 (2003), 3693-3694
- DOI: https://doi.org/10.1090/S0002-9939-03-07200-9
- Published electronically: July 9, 2003
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Abstract:
Using Stegall’s variational principle, we present a simple proof of Pitt’s theorem that bounded linear operators from $\ell _q$ into $\ell _p$ are compact for $1\le p<q<+\infty$.References
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Bibliographic Information
- M. Fabian
- Affiliation: Mathematical Institute, Czech Academy of Sciences, Žitná 25, 11567 Praha 1, Czech Republic
- MR Author ID: 64760
- Email: fabian@math.cas.cz
- V. Zizler
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada
- Email: vzizler@math.ualberta.ca
- Received by editor(s): April 6, 2001
- Published electronically: July 9, 2003
- Additional Notes: Supported by grants GA ČR 201-98-1449, AV 1019003, and NSERC 7926
- Communicated by: Jonathan M. Borwein
- © Copyright 2003 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 3693-3694
- MSC (2000): Primary 46B25
- DOI: https://doi.org/10.1090/S0002-9939-03-07200-9
- MathSciNet review: 1998188