Scalable frames in Tensor Product Of Hilbert Spaces

Tight frames are very similar to orthonormal bases and can be used as a good alternative to them. Scaling frames are introduced as a method to transform a general frame to a tight one. This paper investigates in under what conditions the tensor product of two frames is a scalable frame. We expand some results concerning frame operations of eigenvalues to tensor product of Hilbert spaces. Finally, we will show that if one of the frames is scalable, better conditions are obtained for the approximation of tensor product of frames that is not scalable.