Frames and Bases in Tensor Product of Hilbert Spaces
In this article we develop a theory for frames in tensor product of Hilbert spaces. We show that like bases if Y_1, Y_2, ⋅ ⋅ ⋅, Y_n are frames for H_1,H_2, ⋅ ⋅ ⋅, H_n, respectively, then Y_1⊗Y_2⊗...⊗Y_n is a frame for H_⊗1H_2⊗ ⋅ ⋅ ⋅ ⊗H_n. Moreover we consider the canonical dual frame in tensor product space. We further obtain a relation between the dual frames in Hilbert spaces, and their tensor product.