On the J -reflexive operators

Abstract

A bounded linear operator T on a Banach space X is J -reflexive if every bounded operator on X thatleaves invariant the sets J(T, x) for all x is contained in the closure of orb(T) in the strong operator topology. Wediscuss some properties of J -reflexive operators. We also give and prove some necessary and sufficient conditions underwhich an operator is J -reflexive. We show that isomorphisms preserve J -reflexivity and some examples are considered.Finally, we extend the J -reflexive property in terms of subsets.