N Infinite Dimensional Quadratic Volterra Operators

Details N Infinite Dimensional Quadratic Volterra Operators N Infinite Dimensional Quadratic Volterra Operators

2005-10-16

arxiv.org/abs/math/0510338v1

Jour. Math. Anal. Appl. 310(2005), 533--556

Mathematics

Functional Analysis

21 pages

Scientific paper

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.

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