Distances between Banach spaces

Details Distances between Banach spaces Distances between Banach spaces

1997-09-08

arxiv.org/abs/math/9709211v1

Forum Math., 11 (1999), 17-48

Mathematics

Functional Analysis

Scientific paper

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 $d(B_X,B_Y)$ 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-Hausdorff distance which is defined to be the infimum 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 applications to the theory of complex interpolation.

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