# Subspace-diskcyclic sequences of linear operators

**Journal**: Sahand Communications in Mathematical Analysis (Vol.8, No. 1)

**Publication Date**: 2017-10-01

**Authors** : Mohammad Reza Azimi;

**Page** : 97-106

**Keywords** : Sequences of operators; Diskcyclic vectors; Subspace-diskcyclicity; Subspace-hypercyclicity;

### Abstract

A sequence ${T_n}_{n=1}^{infty}$ of bounded linear operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of this paper is the studying of subspace diskcyclic sequence of operators like as the well known results in a single operator case. In the first section of this paper, we study some conditions that imply the diskcyclicity of ${T_n}_{n=1}^{infty}$. In the second section, we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by some authors in cite{MR1111569, MR2261697, MR2720700}) which are sufficient for the sequence ${T_n}_{n=1}^{infty}$ to be subspace-diskcyclic(subspace-hypercyclic).

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Last modified: 2018-02-03 20:15:01