Turkish Journal of Mathematics
Abstract
A bounded linear operator $T$ on a Banach space $X$ is $J$-reflexive if every bounded operator on $X$ that leaves invariant the sets $J(T,x)$ for all $x$ is contained in the closure of $orb(T)$ in the strong operator topology. We discuss some properties of $J$-reflexive operators. We also give and prove some necessary and sufficient conditions under which 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.
DOI
10.3906/mat-1707-9
Keywords
Orbit of an operator, $J$-sets, $J^{mix} $-sets, $J$-class operator, reflexive operator
First Page
1795
Last Page
1802
Recommended Citation
HOSSEINI, P. S, & YOUSEFI, B (2018). On the $J$-reflexive operators. Turkish Journal of Mathematics 42 (4): 1795-1802. https://doi.org/10.3906/mat-1707-9
