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Forum Mathematicum

Managing Editor: Brüdern, Jörg

Editorial Board Member: Bruinier, Jan Hendrik / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Gallavotti, Giovanni / Garnier, Josselin / Neeb, Karl-Hermann / Noguchi, Junjiro / Ranicki, Andrew / Segal, Dan / Shahidi, Freydoon / Shigekawa, Ichiro / Sogge, Christopher D. / Strambach, Karl

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Distances between Banach spaces

Citation Information: Forum Mathematicum. Volume 11, Issue 1, Pages 17–48, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: 10.1515/form.11.1.17, March 2008

Publication History

Received:
1997-04-01
Published Online:
2008-03-11

Abstract

The main object of the paper is to study the distance between Banach spaces introduced by Kadets. For Banach spaces X and Y, the Kadets distance is defined to be the infimum of the Hausdorff distance d (BX, BY) between the respective closed unit balls over all isometric linear embeddings of X and Y into a common Banach space Z. This is compared with the Gromov-Hausdorff distance which is defined to be the infimum of d (BX, BY) over all isometric embeddings into a common metric space Z. We prove continuity type results for the Kadets distance including a result that shows that this notion of distance has applications to the theory of complex interpolation.

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