About Subspace-Frequently Hypercyclic Operators

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is subspace-frequently hypercyclic. Additionally, operators on finite spaces can not  be subspace-frequently hypercyclic.