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Hahn-Banach operators | | M.I. Ostrovskii
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6 Mar 2002 | | Journal: | Proceedings of the American Mathematical Society, Vol. 129 (2001), 2923-2930 | | Subject: | Functional Analysis MSC-class: 46B20; 47A20 | math.FA | | Abstract: | We consider real spaces only. Definition. An operator $T:X o Y$ 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 $ ilde 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 $T:X o Y$ of rank $k$. The latter result is a generalization of a recent result due to B.L. Chalmers and B. Shekhtman. | | Source: | arXiv, math.FA/0203055 | | Services: | Forum | Review | PDF | Favorites | |
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