Quotients of Banach spaces of cotype q q Academic Article

Let Z Z be a Banach space and let X Z X subset Z be a B B -convex subspace (equivalently, assume that X X does not contain l 1 n l_1^n s uniformly). Then every Bernoulli series n = 1 n z n Sigma _{n = 1}^infty {varepsilon _n}{z_n} which converges almost surely in the quotient Z / X Z/X can be lifted to a Bernoulli series a.s. convergent in Z Z . As a corollary, if Z Z is of cotype q q , then Z / X Z/X is also of cotype q q . This extends a result of [4] concerning the particular case Z = L 1 Z = {L_1} .