Abstract
We show that the Banach-Mazur distance betweenN-dimensional symmetric spacesE andF satisfies\(d(E,F) \leqq c\sqrt N \), wherec is a numerical constant. IfE is a symmetric space, then\(d(E,l_2^{dim E} ) \leqq 2\sqrt 2 \) max (M (2)(E),M (2)(E)), whereM (2)(E) (resp.M (2)(E)) denotes the 2-convexity (resp. the 2-concavity) constant ofE. We also give an example of a spaceF with an 1-unconditional basis and enough symmetries that satisfiesd(F, l dimF2 )=M (2)(F)M (2)(F).
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Partially supported by NSF Grant MCS-8201044.
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Tomczak-Jaegermann, N. The Banach-Mazur distance between symmetric spaces. Israel J. Math. 46, 40–66 (1983). https://doi.org/10.1007/BF02760622
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DOI: https://doi.org/10.1007/BF02760622