Hahn-Banach operators
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Abstract:
We consider real spaces only. Definition. An operator $T:X\to Y$ between Banach spaces $X$ and $Y$ is called a Hahn-Banach operator if for every isometric embedding of the space $X$ into a Banach space $Z$ there exists a norm-preserving extension $\tilde T$ of $T$ to $Z$. A geometric property of Hahn-Banach operators of finite rank acting between finite-dimensional normed spaces is found. This property is used to characterize pairs of finite-dimensional normed spaces $(X,Y)$ such that there exists a Hahn-Banach operator $T:X\to Y$ of rank $k$. The latter result is a generalization of a recent result due to B. L. Chalmers and B. Shekhtman.References
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Additional Information
- M. I. Ostrovskii
- Affiliation: Department of Mathematics, University of California, Riverside, California 92521-0135
- Address at time of publication: Department of Mathematics, The Catholic University of America, Washington, DC 20064
- MR Author ID: 211545
- Email: ostrovskii@cua.edu
- Received by editor(s): February 9, 2000
- Published electronically: February 22, 2001
- Communicated by: Jonathan M. Borwein
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2923-2930
- MSC (2000): Primary 46B20, 47A20
- DOI: https://doi.org/10.1090/S0002-9939-01-06037-3
- MathSciNet review: 1840095