On the convergence of galerkin approximations (1970)
Let X be a separable Banach space over the reals and let X· be its dual. If x ϵ  X and u ϵ X* we will write and lt;x, u and gt; instead of u (x).  Also, if P: X → X is a linear operator we will denote by  P* the adjoint from X* into X* which is defined by and lt;x, P* u and gt; = and lt;P x, u and gt;. The strong convergence in X will be denoted by xn → x, the weak convergence in X by xnw → x and the w* - convergence in X* by  xnw*→ x.We sat that X has property (B) if there is a sequence { Pn } of bounded linear operator from X into itself such that,