Distances between Banach spaces
نویسندگان
چکیده
Abstraca. The main object of the paper is to study the distance betwecn Banach spaces introduced by Kadets. For Banach spaccs Xand y. thc lGders distancc is denned to be rhe infimum of the Hausdorfl distance d(Bx, rr) betwecn the respoctive closed unit balls over all isomctric linear embeddings of f and yinto a common Banach space Z. This is comparcd with the Gromov-Hausdorff distance which is defined to be the infimum of r1(Br, Br) over all isometric embeddings into a common metric space Z. We prove continuity typc results for thc Kaders distance including a result that shows that this notion of distance has applications to the theory of complex interpolation.
منابع مشابه
m at h . FA ] 8 S ep 1 99 7 DISTANCES BETWEEN BANACH SPACES
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 def...
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