Direct sums of Cartan factors
Direkte Integrale von Hilbertalgebren.
Discrete group actions and the minimal primal ideal space.
Discrete groups with Kazhdan' s property T and factorization property are residually finite.
Disintegration theory on a constant field of non-seperable Hilbert spaces.
Distance between states and statistical inference in quantum theory
Distances between Hilbertian operator spaces
We compute the completely bounded Banach-Mazur distance between different finite-dimensional homogeneous Hilbertian operator spaces.
Ditkin sets in homogeneous spaces
Ditkin sets for the Fourier algebra A(G/K), where K is a compact subgroup of a locally compact group G, are studied. The main results discussed are injection theorems, direct image theorems and the relation between Ditkin sets and operator Ditkin sets and, in the compact case, the inverse projection theorem for strong Ditkin sets and the relation between strong Ditkin sets for the Fourier algebra and the Varopoulos algebra. Results on unions of Ditkin sets and on tensor products are also given.
Division Rings and Group von Neumann Algebras.
Domination of operators in the non-commutative setting
We consider majorization problems in the non-commutative setting. More specifically, suppose E and F are ordered normed spaces (not necessarily lattices), and 0 ≤ T ≤ S in B(E,F). If S belongs to a certain ideal (for instance, the ideal of compact or Dunford-Pettis operators), does it follow that T belongs to that ideal as well? We concentrate on the case when E and F are C*-algebras, preduals of von Neumann algebras, or non-commutative function spaces. In particular, we show that, for C*-algebras...
Double Operator Integrals and Submajorization
We present a user-friendly version of a double operator integration theory which still retains a capacity for many useful applications. Using recent results from the latter theory applied in noncommutative geometry, we derive applications to analogues of the classical Heinz inequality, a simplified proof of a famous inequality of Birman-Koplienko-Solomyak and also to the Connes-Moscovici inequality. Our methods are sufficiently strong to treat these...
Dressing transformation on quantum compact groups
Dual spaces of JB*-triples and the Radon-Nikodym property.
Duality in the theory of crossed products.
Dynamical entropy of a non-commutative version of the phase doubling
A quantum dynamical system, mimicking the classical phase doubling map on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.