prasenjit ghosh

The notion of a K-frame in n-Hilbert space is presented and some of their characterizations are given. We establish stability condition of K-frame in n-Hilbert space under some perturbations. We verify that sum of two K-frames is also a K-frame in n-Hilbert space. Also, the concept of tight K-frame in n-Hilbert space is described and some properties of its are going to be established.

We study the concept of frame in tensor product of  $n$-Hilbert spaces as tensor product of  $n$-Hilbert spaces is again an  $n$-Hilbert space. We generalize some of the known results about bases to frames in this new Hilbert space. A relationship between frame and bounded linear operator in tensor product of  $n$-Hilbert spaces is studied. Finally,;the dual frame in tensor product of  $n$-Hilbert spaces is discussed.