Subspace-diskcyclic sequences of linear operators (1409.2635v1)

Abstract: A sequence ${T_n}{n=1}^{\infty}$ of bounded linear operators between separable Banach spaces $X, Y$ is called diskcyclic if there exists a vector $x\in X$ such that the disk-scaled orbit ${\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1}$ is dense in $Y$. In the first section of this paper we study some conditions that imply the diskcyclicity of ${T_n}{n=1}^{\infty}$. In particular, a sequence ${T_n}{n=1}^{\infty}$ of bounded linear operators on separable infinite dimensional Hilbert space $\mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $M\subseteq \mathcal{H},$ if there exists a vector $x\in \mathcal{H}$ such that the disk-scaled orbit ${\alpha T_n x: n\in \mathbb{N}, \alpha \in\mathbb{C}, | \alpha | \leq 1}\cap M$ is dense in $M$. In the second section we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by the some mathematicians in \cite{MR2261697, MR2720700, MR1111569}) which are sufficient for the sequence ${T_n}{n=1}^{\infty}$ to be subspace-diskcyclic.