We consider the Aluthge transform T̃ = |T |1/2U |T |1/2 of a Hilbert space operator T , where T = U |T | is the polar decomposition of T . We prove that the map T 7→ T̃ is continuous with respect to the norm topology and with respect to the ∗–SOT topology on bounded sets. We consider the special case in a tracial von Neumann algebra when U implements an automorphism of the von Neumann algebra gen...

We consider the Alugthe transform T̃ = |T |1/2U |T |1/2 of a Hilbert space operator T , where T = U |T | is the polar decomposition of T . We prove that the map T 7→ T̃ is continuous with respect to the norm topology and with respect to the ∗–SOT topology. For T in a tracial von Neumann algebra, we show that the Brown measure is unchanged by the Aluthge transform. We consider the special case whe...

Cipriani and Sauvageot have shown that for any [Formula: see text]-generator text] of a tracially symmetric quantum Markov semigroup on C*-algebra there exists densely defined derivation from to Hilbert bimodule such text]. Here, we show this construction can in general not be generalized semigroups are with respect non-tracial state. In particular, all derivations bimodules assumed concrete fo...

Let A be a unital simple separable C∗-algebra with strict comparison of positive elements. We prove that the Cuntz semigroup of A is recovered functorially from the Murray–von Neumann semigroup and the tracial state space T(A) whenever the extreme boundary of T(A) is compact and of finite covering dimension. Combined with a result of Winter, we obtain Z ⊗ A ∼= A whenever A moreover has locally ...

We prove a central limit theorem for non-commutative random variables in a von Neumann algebra with a tracial state: Any non-commutative polynomial of averages of i.i.d. samples converges to a classical limit. The proof is based on a central limit theorem for ordered joint distributions together with a commutator estimate related to the Baker-Campbell-Hausdorff expansion. The result can be cons...

This short note is an appendix to [6]. Let θ ∈ R. Denote by Aθ the rotation C∗-algebra generated by unitaries U and V subject to UV = eV U , and by Aθ its canonical smooth subalgebra. Denote by tr the canonical faithful tracial state on Aθ determined by tr(U V ) = δm,0δn,0 for all m,n ∈ Z. Denote by δ1 and δ2 the unbounded closed ∗-derivations of Aθ defined on some dense subalgebras of Aθ and d...

In this paper, we generalize Haagerup’s inequality [H] (on convolution norm in the free group) to a very general context of R-diagonal elements in a tracial von Neumann algebra; moreover, we show that in this “holomorphic” setting, the inequality is greatly improved from its originial form. We give an elementary combinatorial proof of a very special case of our main result, and then generalize ...

We establish the tracial stability of a certain class graph products C*-algebras. This result involves development pincushion finite graphs. then apply this in two ways. The first application yields selective version Lin's Theorem for almost commuting operators. second addresses some approximation properties right-angled Artin groups. In particular, we show that full C*-algebra any group is qua...

We investigate connections between actions on separable C?-algebras with Rokhlin-type properties and absorption of the Jiang-Su algebra Z. show that if A admits an approximately inner group action finite Rokhlin dimension commuting towers then is Z-stable. obtain analogous results for tracial version property approximate innerness. Going beyond innerness, a single automorphism which have are al...

We study embeddings of tracial $\mathrm{W}^*$-algebras into a ultraproduct matrix algebras through an amalgamation free probabilistic and model-theoretic techniques. Jung implicitly Hayes explicitly defined \emph{$1$-bounded entropy} the asymptotic covering numbers Voiculescu's microstate spaces, that is, spaces tuples $(X_1^{(N)},X_2^{(N)},\dots)$ having approximately same $*$-moments as gener...