For a Banach space X over the reals, J. Gao defined certain constants for X, the main ones being g(X) = infkxk=1infkyk=1 max{kx−yk, kx+yk}, G0(X) = supkxk=1supkyk=1 min{kx−yk, kx+yk}. By relating these to the modulus of convexity through the form given by V. D. Milman, we give results concerning uniformly nonsquare spaces. The value of these constants is also calculated for lp spaces (1 < p < 1).
About some parameters of normed linear spaces.
CASINI, EMANUELE GIUSEPPE
1986-01-01
Abstract
For a Banach space X over the reals, J. Gao defined certain constants for X, the main ones being g(X) = infkxk=1infkyk=1 max{kx−yk, kx+yk}, G0(X) = supkxk=1supkyk=1 min{kx−yk, kx+yk}. By relating these to the modulus of convexity through the form given by V. D. Milman, we give results concerning uniformly nonsquare spaces. The value of these constants is also calculated for lp spaces (1 < p < 1).
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