Relative boundedness and relative compactness for linear operators in Banach spaces
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- by P. Binding and R. Hryniv PDF
- Proc. Amer. Math. Soc. 128 (2000), 2287-2290 Request permission
Abstract:
If $A$ and $B$ are linear operators acting between Banach spaces, we show that compactness of $B$ relative to $A$ does not in general imply that $B$ has $A$-bound zero. We do, however, give conditions under which the above implication is valid.References
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Additional Information
- P. Binding
- Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
- Email: binding@ucalgary.ca
- R. Hryniv
- Affiliation: Institute for Applied Problems of Mechanics and Mathematics, 3b Naukova str., 290601 Lviv, Ukraine
- Email: hryniv@mebm.lviv.ua
- Received by editor(s): July 24, 1998
- Published electronically: March 29, 2000
- Additional Notes: The first author’s research was supported by NSERC of Canada.
The second author acknowledges appointment as a Post Doctoral Fellow of the Pacific Institute for the Mathematical Sciences at the University of Calgary. - Communicated by: David R. Larson
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 2287-2290
- MSC (2000): Primary 47A55, 47B07
- DOI: https://doi.org/10.1090/S0002-9939-00-05729-4
- MathSciNet review: 1756088