Subspace super-recurrence of operators

Abstract

This paper is a continuation of our recent work on super-recurrence of operators \cite{ABf}.We introduce and study subspace super-recurrence of operators.We give the relationship between this new class of operators, super-recurrent operators, and other well known class of operators of linear topological dynamics.Several examples and proprieties are given.In particular, we give the relationship between subspace super-recurrence of an operator $T$ and the set of its eigenvectors.Also we presented some sufficient conditions of subspacesuper-recurrence and we demonstrate a subspace super-recurrence criterion.As application, we study the case of shifts operators.