Space c_0

let y= (eta_j), eta_j element of C (complex numbers) be such that

sum psi_i eta_j converges for every x=(psi_j0 element of c_0, where

c_0 contained in l^{\infty} is the subspace of all complex sequences converging to zero.

Show that sum |eta_j| < \infty. Use the Uniform Boundedness theorem.