2002/03/06 by M. I. Ostrovskii
Mathematics · #math.FA #msc:46B20 #msc:47A20
published as Proceedings of the American Mathematical Society, Vol. 129 (2001), 2923-2930
arxiv created 2002/03/06 · arxiv updated 2009/11/30
We consider real spaces only. Definition. An operator T:X→ 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 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→ Y of rank k. The latter result is a generalization of a recent result due to B.L. Chalmers and B. Shekhtman.