Entropy of shifts on topological graph -algebras.
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.
The generalized non-commutative torus of rank n is defined by the crossed product , where the actions of ℤ on the fibre of a rational rotation algebra are trivial, and is a non-commutative torus . It is shown that is strongly Morita equivalent to , and that is isomorphic to if and only if the set of prime factors of k is a subset of the set of prime factors of p.
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.