Tensor Product K-Dual Frames

Abstract

Let H1 and H2 be two separable Hilbert spaces, K1∈ B(H1) and K2∈ B(H2) . Based on some previous results about tensor product of frames, in this paper we generalize them to tensor product of K-frames. We provide equivalent conditions for that the tensor product of two K1 -frame and K2 -frame is a K1⊗ K2 -frame. Moreover, we investigate whenever the tensor product of two Bessel sequences F and G in H1 and H2 , respectively, is a K1⊗ K2 -dual frame for F⊗ G . © 2023, The Author(s), under exclusive licence to Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia.