The Size of the Unit Sphere
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 450-455
Voir la notice de l'article provenant de la source Cambridge University Press
Banach (1, pp. 242-243) defines, for two Banach spaces X and Y, a number (X, Y) = inf (log (‖L‖ ‖L -1‖)), where the infimum is taken over all isomorphisms L of X onto F. He says that the spaces X and Y are nearly isometric if (X, Y) = 0 and asks whether the concepts of near isometry and isometry are the same; in particular, whether the spaces c and c 0, which are not isometric, are nearly isometric. In a recent paper (2) Michael Cambern shows not only that c and c0 are not nearly isometric but obtains the elegant result that for the class of Banach spaces of continuous functions vanishing at infinity on a first countable locally compact Hausdorff space, the notions of isometry and near isometry coincide.
Whitley, Robert. The Size of the Unit Sphere. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 450-455. doi: 10.4153/CJM-1968-041-1
@article{10_4153_CJM_1968_041_1,
author = {Whitley, Robert},
title = {The {Size} of the {Unit} {Sphere}},
journal = {Canadian journal of mathematics},
pages = {450--455},
year = {1968},
volume = {20},
number = {1},
doi = {10.4153/CJM-1968-041-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1968-041-1/}
}
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