Frame Operator and Hilbert-Schmidt Operator in Tensor Product of Hilbert Spaces

Abstract

Abstract The tensor product of frames in Hilbert spaces is introduced. It was shown that the tensor product of two frames is a frame for the tensor product of Hilbert spaces. The concept of tensor frame operator on tensor product of Hilbert space is given and results of it are presented. Inequalities between tensor product of frames and the Hilbert-Schmidt operators are established.