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Turkish Journal of Mathematics

DOI

10.3906/mat-1904-183

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

First Page

2371

Last Page

2376

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