Open AccessOn Subspace-recurrent Operators
Author(s) -
Mansooreh Moosapoor
Publication year - 2021
Publication title -
tamkang journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.324
H-Index - 18
eISSN - 0049-2930
pISSN - 2073-9826
DOI - 10.5556/j.tkjm.53.2022.3579
Subject(s) - subspace topology , mathematics , transitive relation , invertible matrix , operator (biology) , discrete mathematics , random subspace method , invariant subspace problem , set (abstract data type) , combinatorics , pure mathematics , banach space , mathematical analysis , finite rank operator , unbounded operator , computer science , biochemistry , chemistry , repressor , transcription factor , gene , programming language
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.