Spectral and ergodic properties of completely positive maps and decoherence

In an attempt to propose more general conditions for decoherence occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital C⁎-algebras, with a particular focus gapped which the transient portion arising dynamical system can be separated from persistent one. After some results, first devote our attention abelian case by investigating ⁎-endomorphisms of, in non-unital, their structure. The finite-dimensional is also investigated detail, examples are provided part associated equipped new product making it into C⁎-algebra, map under consideration restricts ⁎-automorphism this C⁎-structure, thus generating conservative dynamics that part.