Tensor product of Schauder frames and besselian Schauder frames of Banach spaces

Abstract

We introduce the tensor product of besselian sequences and besselian Schauder frames in tensor product of separable Banach spaces. We prove that the tensor product of two besselian sequences (resp. besselian Schauder frames) is a besselian sequence (resp. a besselian Schauder frame) if one of the two sequences is rectangular. On the other hand we give an example for which the tensor product of two besselain Schauder frames is not besselain Schauder frame.