In this paper, we introduce and study the notion of super-recurrence operators. We investigate some properties class operators show that it shares characteristics with supercyclic recurrent particular, if T is super-recurrent, then ?(T) ?p(T*), spectrum point T* respectively, have noteworthy properties.

Bounded weighted composition operators, as well compact on Fock spaces have been characterised. This characterisation is refined to the extent that question of whether operators space can be supercyclic answered in negative.

We study hypercyclicity properties of functions of Banach space operators. Generalizations of the results of Herzog-Schmoeger and Bermudez-Miller are obtained. As a corollary we also show that each non-trivial operator commuting with a generalized backward shift is supercyclic. This gives a positive answer to a conjecture of Godefroy and Shapiro. Furthermore, we show that the norm-closures of t...

Abstract. By the well-known result of Brown, Chevreau and Pearcy, every Hilbert space contraction with spectrum containing the unit circle has a nontrivial closed invariant subspace. Equivalently, there is a nonzero vector which is not cyclic. We show that each power bounded operator on a Hilbert space with spectral radius equal to one has a nonzero vector which is not supercyclic. Equivalently...