Subspace-diskcyclic sequences of linear operators

A sequence {Tn}∞n=1 of bounded linear operators on a separable infinite dimensional Hilbert space H is called subspace￾diskcyclic with respect to the closed subspace M ⊆ H, if there exists a vector x ∈ H such that the disk-scaled orbit {αTnx : n ∈ N, α ∈ C, |α| ≤ 1} ∩ 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 {Tn}∞n=1. In the second section, we survey some conditions and subspace-diskcyclicity criterion (analogue the results obtained by some authors in [6, 10, 11]) which are sufficient for the sequence {Tn} ∞n=1 to be subspace-diskcyclic(subspace-hypercyclic).

Keywords:

Sequences of operators , Diskcyclic vectors , Subspace-diskcyclicity , Subspace-hypercyclicity