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