Introduction to Continuous biframes in Hilbert spaces and their tensor products

Abstract

We introduce the notion of a continuous biframe in a Hilbert space which is a generalization of discrete biframe in Hilbert space. Representation theorem for this type of generalized frame is verified and some characterizations of this biframe with the help of a invertible operator is given. Here we also introduce the concept of continuous biframe for the tensor products of Hilbert spaces and give an example. Further, we study dual continuous biframe and continuous biframe Bessel multiplier in Hilbert spaces and their tensor products.