A characterization of Riesz bases and pair of dual frames in tensor product of Hilbert spaces.

This paper characterize important concepts such as the Riesz bases and pair of dual frames for tensor product of Hilbert spaces and introduce some special properties of pair of dual frames in these spaces. We show that Riesz bases and pair of dual frames in H ⊗ K are preserved under invertible and unitary operators on H . Finally, We present a representation for Hilbert–Schmidt operators by a pair of dual frames. [ABSTRACT FROM AUTHOR]