# Journal of Operator Theory

Volume 70, Issue 1, Summer 2013 pp. 181-190.

Quasi-representations of Finsler modules over $C^*$-algebras**Authors**: Maryam Amyari (1), Mahnaz Chakoshi (2), and Mohammad Sal Moslehian (3)

**Author institution:**(1) Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran

(2) Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad 91735, Iran

(3) Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P.O. Box 1159, Mashhad 91775, Iran

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

**DOI:**http://dx.doi.org/10.7900/jot.2011may20.1929

**Keywords:**Finsler module, $C^*$-algebra, $\varphi$-morphism, quasi-representation, nondegenerate quasi-representation, irreducible quasi-representation

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