Some remarks on C*-algebras associated with certain topologicalMarkov chains.
Spectra of actions on type I C*-algebras.
Spectral Pairs in Cartesian Coordinates.
Spontaneously broken symmetries
Square functions, bounded analytic semigroups, and applications
To any bounded analytic semigroup on Hilbert space or on -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative -spaces, Banach lattices, and their subspaces. We give some applications to functional calculus, similarity problems, multiplier theory, and control theory.
Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras
We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math....
Stable rank and real rank of compact transformation group C*-algebras
Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.
Standard and split inclusions of von Neumann algebras.
Subproduct systems.
Sur le type du produit croisé d'une algèbre de von Neumann par un groupe localement compact
Sur les semigroupes dynamiques quantiques
Systèmes dynamiques non commutatifs et moyennabilité.
Takesaki's duality for a non-degenerate co-action.
The action of groups on real factors of type III, .
The adic realizations of the ergodic actions with the homeomorphisms of the Markov compact and the ordered Bratteli diagrams
The C*-algebras of codimension one foliations without holonomy.
The cyclic homology of crossed product algebras.
The cyclic homology of crossed product algebras, II. Topological algebras.
The graph traces of finite graphs and applications to tracial states of -algebras.
The intrinsic invariant of an approximately finite dimensional factor and the cocycle conjugacy of discrete amenable group actions.