Quasi-representations of Finsler modules over C*-algebras

We show that every Finsler module over a $C^{\ast }$-algebra has a quasi-representation into the Banach space $\mathbb{B}(\mathcal{H},\mathcal{K})$ of all bounded linear operators between some Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$. We define the notion of completely positive $\phi$-morphism and establish a Stinespring type theorem in the framework of Finsler modules over $C^{\ast }$-algebras. We also investigate the nondegeneracy and the irreducibility of quasi-representations.