Some properties of Gurarii's modulus of convexity

In 1967 Gurarii introduces a modulus of convexity, beta(E)(epsilon). In this paper some properties of this modulus are analyzed. They have their analogous on the well known- Clarkson's modulus of convexity, delta(E)(epsilon) In particular we show that beta(E)(epsilon) can be defined in several equivalent forms. We also prove that in l(p) spaces with 2 < p the Gurarii's modulus satifies the equality beta(lp) (epsilon) = 1 - (p)root 1-(epsilon/2)(p) for 0 less than or equal to epsilon less than or equal to 2.