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).