2-K-Frames in 2-Hilbert Spaces

The aim of this article, we introduce a 2-K-frames in the 2-Hilbert space H, where K is a θ-bounded linear operator on H for a fixed element θ in H, and explore some properties of them. Also, we will characterize the 2-Kframes by the 2 pre-K-frame operators, the 2-K-frame operators, likewise to what is seen in the case of Hilbert spaces. In the rest of the article, we will set a definition of θ-atomic systems for K, and give some results concerning this notion. Finally we will find out a representation of each element in a closed range R(K).