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Ergodic Dilation of a Quantum Dynamical System

Carlo Pandiscia (2014)

Confluentes Mathematici

Using the Nagy dilation of linear contractions on Hilbert space and the Stinespring’s theorem for completely positive maps, we prove that any quantum dynamical system admits a dilation in the sense of Muhly and Solel which satisfies the same ergodic properties of the original quantum dynamical system.

Generalized non-commutative tori

Chun-Gil Park (2002)

Studia Mathematica

The generalized non-commutative torus T ϱ k of rank n is defined by the crossed product A m / k × α × α . . . × α , where the actions α i of ℤ on the fibre M k ( ) of a rational rotation algebra A m / k are trivial, and C * ( k × k ) × α × α . . . × α is a non-commutative torus A ϱ . It is shown that T ϱ k is strongly Morita equivalent to A ϱ , and that T ϱ k M p is isomorphic to A ϱ M k ( ) M p if and only if the set of prime factors of k is a subset of the set of prime factors of p.

Half-liberated real spheres and their subspaces

Julien Bichon (2016)

Colloquium Mathematicae

We describe the quantum subspaces of Banica-Goswami's half-liberated real spheres, showing in particular that there is a bijection between the symmetric ones and the conjugation stable closed subspaces of the complex projective spaces.

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