Let $A$ be a unital simple $A\mathbb{T}$-algebra of real rank zero. Given an order two automorphism $h: K\_1(A)\to K\_1(A)$, we show that there is $\alpha$: $A\to A$ such $\alpha\_{\*0}=\mathrm {id}$, $\alpha\_{1}=h$ and the action $\mathbb{Z}\_2$ generated by $\alpha$ has tracial Rokhlin property. Consequently, $C^(A,\mathbb{Z}\_2,\alpha)$ AH-algebra with no dimension growth, Thus our main res...

Let M be a closed connected manifold and let D be an elliptic operator on M . Let G be a discrete countable group and let M̃ → M be a principal G-bundle. Connes and Moscovici showed that this data defines an analytic index ind`1(G)(D) ∈ K0(`(G)). If B is a unital tracial C*-algebra, we give a formula for the trace of the image of ind`1(G)(D) in K0(B) under the map induced by a quasi-representati...

We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in non-commuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. We prove that such a sequence can be represented with tracial moments of matrices if its corresponding moment matrix is positive semidefini...

We consider unital simple inductive limits of generalized dimension drop C∗-algebras They are so-called ASH-algebras and include all unital simple AH-algebras and all dimension drop C∗-algebras. Suppose that A is one of these C∗-algebras. We show that A ⊗ Q has tracial rank no more than one, where Q is the rational UHF-algebra. As a consequence, we obtain the following classification result: Le...

We give examples of minimal diffeomorphisms of compact connected manifolds which are not topologically orbit equivalent, but whose transformation group C*-algebras are isomorphic. The examples show that the following properties of a minimal diffeomorphism are not invariants of the transformation group C*-algebra: having topologically quasidiscrete spectrum; the action on singular cohomology (wh...

X iv :0 70 9. 42 29 v1 [ m at h. FA ] 2 6 Se p 20 07 An Extrapolation of Operator Valued Dyadic Paraproducts Tao MEI 1 Abstract We consider the dyadic paraproducts πφ on T associated with an M-valued function φ. Here T is the unit circle and M is a tracial von Neumann algebra. We prove that their boundedness on L(T, L(M)) for some 1 < p < ∞ implies their boundedness on L(T, L(M)) for all 1 < p ...

The tracial analog of Hilbert’s classical result on positive binary quartics is presented: a trace-positive bivariate noncommutative polynomial of degree at most four is a sum of hermitian squares and commutators. This is applied via duality to investigate the truncated tracial moment problem: a sequence of real numbers indexed by words of degree four in two noncommuting variables with values i...

Using Voiculescu’s notion of a matricial microstate we introduce fractal dimensions and entropy for finite sets of self-adjoint operators in a tracial von Neumann algebra. We show that they possess properties similar to their classical predecessors. We relate the new quantities to free entropy and free entropy dimension and show that a modified version of free Hausdorff dimension is an algebrai...

We show that, if A is a separable simple unital C-algebra which absorbs the Jiang–Su algebra Z tensorially and which has real rank zero and finite decomposition rank, then A is tracially AF in the sense of Lin, without any restriction on the tracial state space. As a consequence, the Elliott conjecture is true for the class of C-algebras as above which, additionally, satisfy the Universal Coeff...

We investigate the tracial and ideal structures of C ? -algebras quasi-regular representations stabilizers boundary actions. Our main tool is notion maps, namely ?-equivariant unital completely positive maps from ?- to ( ? F ? ) , where denotes Furstenberg a group ?. For unitary representation ? coming groupoid germs action, we show that there unique map on . Consequently, describe structure fo...