Subspace-diskcyclic sequences of linear operators

A sequence {T n } ∞ 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 {αT n x:n∈N,α∈C,|α|≤1}∩M {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 {T n } ∞ n=1 . 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 to be subspace-diskcyclic(subspace-hypercyclic).