Scalable frames in Tensor Product Of Hilbert Spaces

Document Type : Research Paper


Department of Mathematics, University of Hormozgan, Bandar Abbas, Iran



‎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.