Subspace-diskcyclic sequences of linear operators

• Main Author: Mohammad Reza Azimi
• Format: Article
• Language: English
• Published: University of Maragheh 2017-10-01
• Series: Sahand Communications in Mathematical Analysis
• Subjects: Sequences of operators; Diskcyclic vectors; Subspace-diskcyclicity; Subspace-hypercyclicity
• Online Access: http://scma.maragheh.ac.ir/article_23850_39a0664f6ddf12b1b192462ffddd7aaf.pdf

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).