Continuous biframes in Hilbert $C^{\ast}-$modules

Abstract

In this paper, we will introduce the concept of a continuous biframe for Hilbert $ C^{\ast}- $modules. Then, we examine some characterizations of this biframe with the help of an invertible and adjointable operator is given. Moreover, we study continuous biframe Bessel multiplier and dual continuous biframe in Hilbert $ C^{\ast}- $modules. Also, we develop the concept of continuous biframes in the tensor product of two Hilbert $C^{\ast}$-modules over a unital $C^{\ast}$-algebra $\mathcal{A}$ and provide some properties of invertible transformed biframes and Bessel multipliers in the tensor product.