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Distances between Banach spaces
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N. J. Kalton
Veröffentlicht/Copyright:
26. August 2025
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 HausdorlT 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.
Published Online: 2025-08-26
Published in Print: 1999-01-01
© 2025 by Walter de Gruyter Berlin/Boston
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Artikel in diesem Heft
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill-Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Contents
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill - Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Instructions to Authors
- Editors
Artikel in diesem Heft
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill-Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Contents
- Some remarks on linear structures in right distributive domains
- Distances between Banach spaces
- p-Extensions of free pro-p groups
- On the Brill - Noether problem for vector bundles
- On 4-dimensional elation Laguerre planes admitting simple Lie groups of automorphisms
- Geometric asymptotics and the logarithmic Sobolev inequality
- Instructions to Authors
- Editors
