On Subspace-recurrent Operators

Abstract

In this article, subspace-recurrent operators are presented and it is showed that the set of subspace-transitive operators is a strict subset of the set of subspace-recurrent operators. We demonstrate that despite subspace-transitive operators and subspace-hypercyclic operators, subspace-recurrent operators exist on finite dimensional spaces. We establish that operators that have a dense set of periodic points are subspace-recurrent. Especially, if $T$ is an invertible chaotic or an invertible subspace-chaotic operator, then $T^{n}$, $T^{-n}$ and $\lambda T$ are subspace-recurrent for any positive integer $n$ and any scalar $\lambda$ with absolute value $1$. Also, we state a subspace-recurrence criterion.

On the Recurrent C 0 -Semigroups, Their Existence, and Some Criteria

“…Proof. It is enough to consider α � 1 in eorem 7 Like eorem 4.1 in [14], we can define another recurrent criterion that is based on dense subsets. □ Theorem 8.…”