Tensor product and scalability of iterated pg-frames in Banach spaces

In this paper, we introduce the structure of the tensor product of iterated [Formula: see text]-frames [Formula: see text], where [Formula: see text] and show that the tensor product of two iterated [Formula: see text]-frames is again a [Formula: see text]-frame. We prove that the invertible image of the tensor product of two iterated [Formula: see text]-frames is again a [Formula: see text]-frame. In addition, we introduce the notion of scalability of the iterated [Formula: see text]-frame [Formula: see text]. We show that scaling an iterated [Formula: see text]-frame by a semi-normalized sequence or a positively confined sequence is again an iterated [Formula: see text]-frame. For a surjective isometry [Formula: see text], we prove that the scalability of the iterated [Formula: see text]-frame [Formula: see text] and [Formula: see text]-frame [Formula: see text] is equivalent. Furthermore, we establish that the tensor product of an iterated scalable [Formula: see text]-frame, with a [Formula: see text]-frame, may not be scalable [Formula: see text]-frame. Lastly, we prove a result that includes a sufficient condition under which the tensor product of two iterated [Formula: see text]-frames [Formula: see text] becomes scalable [Formula: see text]-frame.