Distances between Banach spaces

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 dened to be the inmum of the Hausdor distance d(B X , B Y ) 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-Hausdor distance which is dened to be the inmum of d(B X , B Y ) 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 appli- cations to the theory of complex interpolation. 1991 Mathematics Subject Classication: 46B20, 46M35; 46B03, 54E35.