  In this paper we study a class of quadratic operators named by Volterra
operators on infinite dimensional space. We prove that such operators have
infinitely many fixed points and the set of Volterra operators forms a convex
compact set. In addition, it is described its extreme points. Besides, we study
certain limit behaviors of such operators and give some more examples of
Volterra operators for which their trajectories do not converge. Finally, we
define a compatible sequence of finite dimensional Volterra operators and prove
that any power of this sequence converges in weak topology.
