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2015 Notes about subspace-supercyclic operators
Liang Zhang, Ze-Hua Zhou
Ann. Funct. Anal. 6(2): 60-68 (2015). DOI: 10.15352/afa/06-2-6

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.

Citation

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Liang Zhang. Ze-Hua Zhou. "Notes about subspace-supercyclic operators." Ann. Funct. Anal. 6 (2) 60 - 68, 2015. https://doi.org/10.15352/afa/06-2-6

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1312.47013
MathSciNet: MR3292515
Digital Object Identifier: 10.15352/afa/06-2-6

Subjects:
Primary: 47A16
Secondary: ‎46E15

Rights: Copyright © 2015 Tusi Mathematical Research Group

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Vol.6 • No. 2 • 2015
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