Frame Operator and Hilbert-Schmidt Operator in Tensor Product of Hilbert Spaces

Controlled generalized fusion frame in the tensor product of Hilbert spaces

“…The tensor product of Hilbert spaces H and K is a certain linear space of operators which was presented by Folland [5] and independently by Kadison and Ringrose [11]. Below we give the definition according to [19].…”

“…Frames and bases in the tensor product of Hilbert spaces were introduced by Khosravi and Asgari [12]. Reddy et al [19] studied the frame in the tensor product of Hilbert spaces and presented the tensor frame operator on the tensor product of Hilbert spaces. The concepts of fusion frames and g-frames in the tensor product of Hilbert spaces were introduced by Khosravi and Mirzaee Azandaryani [13].…”

Generalized fusion frame in tensor product of Hilbert spaces

“…Definition 2.11. [17] The tensor product of Hilbert spaces H and K is denoted by H ⊗ K and it is defined to be an inner product space associated with the inner product…”

“…Frames and Bases in Tensor Product of Hilbert spaces were introduced by A. Khosravi and M. S. Asgari [12]. Reddy et al [17] also studied the frame in tensor product of Hilbert spaces and presented the tensor frame operator on tensor product of Hilbert spaces. The concepts of fusion frames and g-frames in tensor product of Hilbert spaces were introduced by Amir Khosravi and M. Mirzaee Azandaryani [13].…”

Tensor Product of 2-Frames in 2-Hilbert Spaces

“…Some results on 2-inner product spaces are described by H. Mazaherl and R. Kazemi [6]. The tensor product of frames in tensor product of Hilbert spaces is introduced by G. Upender Reddy and N. Gopal Reddy [7] and some results on tensor frame operator are presented.…”