On the $J$-reflexive sequences

Authors : Parviz Sadat Hosseini, Bahmann Yousefi

Pages : 2371-2376

View : 10 | Download : 6

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :We call a sequence $\mathcal{T}=(T_n)_n$ of bounded operators on a Banach space $X$, $J$-reflexive if every bounded operator on $X$ that leaves invariant, the $J$-sets of $\mathcal{T}$ is contained in the closure of $\{I, T_1, T_2, ... \}$ in the strong operator topology. We discuss some properties of $J$-reflexive sequences. We also give and prove some sufficient conditions under which an operator sequence is $J$-reflexive. Some examples are considered. Indeed, weakly $J^{mix}$-reflexivity is also defined. Finally, we extend the $J$-reflexive property in terms of subsets.
Keywords : $J$-sets, $J^{mix}$-sets, reflexive operator, strongly bounded below