1. Notes about subspace-supercyclic operators
- Author
-
Liang Zhang and Ze-Hua Zhou
- Subjects
Mathematics::Functional Analysis ,Banach space ,Control and Optimization ,Algebra and Number Theory ,Subspace-Supercyclicity Criterion ,Dense set ,Existential quantification ,Mathematical analysis ,Bounded operator ,Combinatorics ,Subspace-supercyclic ,46E15 ,Orbit (control theory) ,Invariant subspace problem ,47A16 ,Analysis ,Subspace topology ,Mathematics - Abstract
A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic for a nonzero subspace $M$ if $orb\left( {T,x} \right) \cap M$ is dense in $M$ for a vector $x \in X$, where $orb (T,x)=\{T^nx: n=0,1,2,\cdots\}$. Similarly, the bounded linear operator $T$ on a Banach space $X$ is called subspace-supercyclic for a nonzero subspace $M$ if there exists a vector whose projective orbit intersects the subspace $M$ in a relatively dense set. In this paper we provide a Subspace-Supercyclicity Criterion and offer two equivalent conditions of this criterion. At the same time, we also characterize other properties of subspace-supercyclic operators.
- Published
- 2015