Motivated by frame-vector for a unitary system, we study a class of cyclic operatorson a separable Hilbert space which is called frame-cyclic operators. The orbit of suchan operator on some vector, namely frame-cyclic vector, is a frame. Some properties ofthese operators on finite- and infinite-dimensional Hilbert spaces and their relations withcyclic and hypercyclic operators are established. A lower and upper bound for the normof a self-adjoint frame-cyclic operator is obtained. Also, construction of the set of frame-cyclic vectors is considered. Finally, we deal with Kato’s approximation of frame-cyclicoperators and discuss their frame-cyclic properties.

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