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19th December 19:54
External User
Posts: 1

Classification of Banach spaces
If U is any bounded convex balanced (i.e. U = U) open set, the Minkowski
gauge p_U(x) = inf{s: x in sU} is a norm, and conversely any norm is the Minkowski gauge for its unit ball. So the isometric classification for finitedimensional Banach spaces is equivalent to the classification of bounded convex balanced open sets under linear transformations. I think there is too much freedom here to have any really useful parametrization. Robert Israel israel@math.ubc.ca Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 
