The $p$-convexity functor for $L_p(X)$-spaces

A construction for transforming an arbitrary $L_p(X)$-norm on a normed space $E$ into a $p$-convex norm is put forward. By applying this construction to the projective tensor norm, an explicit formula for the maximal $p$-convex $L_p(X)$-norm on $E$ is obtained.
Bibliography: 9 titles.