We extend the notions of irreducibility and periodicity of a stochastic matrix to a unital positive linear map $\Phi$ on a finite-dimensional C*-algebra A and discuss the non-commutative version of the Perron-Frobenius theorem. As an example, positive linear maps on $M_2(C)$ are analyzed.

Irreducible and periodic positive maps

FAGNOLA, FRANCO;
2009

Abstract

We extend the notions of irreducibility and periodicity of a stochastic matrix to a unital positive linear map $\Phi$ on a finite-dimensional C*-algebra A and discuss the non-commutative version of the Perron-Frobenius theorem. As an example, positive linear maps on $M_2(C)$ are analyzed.
Completely positive linear map; irreducible; periodic; Perron-Frobenius’ theorem.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/560168
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