On the J -reflexive sequences

Abstract

We call a sequence We call a sequence $T=(T_n)_n$ of bounded operators on a Banach space X, J -reflexive if every boundedoperator on X that leaves invariant, the J -sets of T is contained in the closure of {I, T1, T2, ...} in the strong operatortopology. We discuss some properties of J -reflexive sequences. We also give and prove some sufficient conditions underwhich an operator sequence is J -reflexive. Some examples are considered. Indeed, weakly Jmix -reflexivity is also defined.Finally, we extend the J -reflexive property in terms of subsets.