Annals of Functional Analysis

Notes about subspace-supercyclic operators

Liang Zhang and Ze-Hua Zhou

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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.

Article information

Source
Ann. Funct. Anal., Volume 6, Number 2 (2015), 60-68.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.afa/1418997766

Digital Object Identifier
doi:10.15352/afa/06-2-6

Mathematical Reviews number (MathSciNet)
MR3292515

Zentralblatt MATH identifier
1312.47013

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Keywords
Subspace-supercyclic Subspace-Supercyclicity Criterion Banach space

Citation

Zhang, Liang; Zhou, Ze-Hua. Notes about subspace-supercyclic operators. Ann. Funct. Anal. 6 (2015), no. 2, 60--68. doi:10.15352/afa/06-2-6. https://projecteuclid.org/euclid.afa/1418997766


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