Showing a limited preview of this publication:
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.
Received: 1997-04-01
Published Online: 2008-03-11
Published in Print: 1999-02-15
© Walter de Gruyter
