Markov triplets on CCR-algebras
نویسندگان
چکیده
The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is de ned by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical su ciency in the non-commutative case. The relation to classical Gaussian Markov triplets is also described. 2000 Mathematics Subject Classi cation. Primary 46L53, 60J10; Secondary 40C05, 81R15.
منابع مشابه
Markov property of Gaussian states of canonical commutation relation algebras
The Markov property of Gaussian states of CCR-algebras is studied. The detailed description is given by the representing block matrix. The proof is short and allows in nite dimension. The relation to classical Gaussian Markov triplets is also described. The minimizer of relative entropy with respect to a Gaussian Markov state has the Markov property. The appendix contains formulas for the relat...
متن کاملFe b 20 09 Markov triplets on CCR - algebras
The paper contains a detailed computation about the algebra of canonical commutation relation, the representation of the Weyl unitaries, the quasi-free states and their von Neumann entropy. The Markov triplet is defined by constant entropy increase. The Markov property of a quasi-free state is described by the representing block matrix. The proof is based on results on the statistical sufficien...
متن کاملZero Product Preserving Linear Maps of Ccr C*-algebras with Hausdorff Spectrum
In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map θ between C*-algebras, with both θ and its inverse θ−1 preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR C*-algebras with Hausdorff spectrum, and in general, some special C*-algebras associated to continuous fields of C*-algebras.
متن کاملOn Higher Real and Stable Ranks for CCR C−algebras
We calculate the real rank and stable rank of CCR algebras which either have only finite dimensional irreducible representations or have finite topological dimension. We show that either rank of A is determined in a good way by the ranks of an ideal I and the quotient A/I in four cases: When A is CCR; when I has only finite dimensional irreducible representations; when I is separable, of genera...
متن کامل2 Lisa Orloff
Suppose G is a second countable, locally compact, Hausdorff groupoid with a fixed left Haar system. Let G/G denote the orbit space of G and C∗(G) denote the groupoid C∗-algebra. Suppose that the isotropy groups of G are amenable. We show that C∗(G) is CCR if and only if G/G is a T1 topological space and all of the isotropy groups are CCR. We also show that C∗(G) is GCR if and only if G/G is a T...
متن کامل