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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Darmon, Henri / Duzaar, Frank / Echterhoff, Siegfried / Gordina, Maria / Neeb, Karl-Hermann / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 11, Issue 1


Distances between Banach spaces

Nigel J Kalton / Mikhail I Ostrovskii
Published Online: 2008-03-11 | DOI: https://doi.org/10.1515/form.11.1.17


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.

About the article

Received: 1997-04-01

Published Online: 2008-03-11

Published in Print: 1999-02-15

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

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