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We show that the nuclear dimension of a (twisted) group C*-algebra of a virtually polycyclic group is finite. This prompts us to make a conjecture relating finite nuclear dimension of group C*-algebras and finite Hirsch length, which we…

This paper uses monads and comonads to establish a certain type of equivalence between two subcategories, one reflective and one coreflective, in a category whose objects represent compactifications of non-compact locally compact Hausdorff…

Approximate morphisms have seen significant study across many areas of mathematics, for instance, in the theory of Absolute (Neighborhood) Retracts in topology, or of almost-commuting unitary matrices in analysis. This paper initiates study…

This sequel to \cite{im2008} uses groupoid technology to provide new proofs of the famous theorems of Mallat \cite[Theorem 1 and 2]{Mall_TAMS89} that extend to much broader contexts than those conceived by Mallat. This work was inspired in…

We generalize the notion of orbit equivalence to the non-commutative setting by introducing a new equivalence relation on groups, which we call von Neumann orbit equivalence (vNOE). We prove the stability of this equivalence relation under…

This work is intended to present the basic properties of $KO$-theory for real $C^*$-algebras and to explain its relationship with complex $K$-theory and with $KR$- theory. Whenever possible we will rely upon proofs in printed literature,…

In this paper we study deformations of $C^*$-algebras that are given as cross-sectional $C^*$-algebras of Fell bundles over locally compact groups $G$. Our deformation comes from a direct deformation of the Fell bundles via certain…

In this paper, we give a complete, two-way characterization, of when a noncommutative crossed product $A \rtimes_\lambda G$ is simple, in the case of $G$ being an FC-hypercentral group. This is a large class of amenable groups that contains…

We introduce the $\ell^1$-ideal intersection property for crossed product C*-algebras. It is implied by C*-simplicity as well as C*-uniqueness. We show that topological dynamical systems of arbitrary lattices in connected Lie groups,…

The subject of this paper are operators represented on a Fock space which act only on the two leading components of the tensor. We unify the constructions from arXiv:math/0702158, arXiv:0709.4334, arXiv:0812.0895, and arXiv:1003.2998, and…

We characterise stable finiteness and pure infiniteness of the essential crossed product of a C*-algebra by an action of an inverse semigroup. Under additional assumptions, we prove a stably finite / purely infinite dichotomy. Our main…

Given a coaction $\delta$ of a locally compact group $G$ on a $\mathrm{C}^*$-algebra $A$, we study the relationship between two different forms of coaction invariance of ideals of $A$ and the ideals of the corresponding crossed product…

Let $n\geq 2$ and $G_n=\mathbb{Z}^n\rtimes SL_n(\mathbb{Z})$. We classify all $G_n$-invariant von Neumann subalgebras in $L(G_n)$. For $n=2$, this gives an alternative proof of the previous result of Jiang-Liu. For $n\geq 3$, this gives the…

We classify all $G$-invariant von Neumann subalgebras in $L(G)$ for $G=\mathbb{Z}^2\rtimes SL_2(\mathbb{Z})$. This is the first result on classifying $G$-invariant von Neumann subalgebras in $L(G)$ for i.c.c. groups $G$ without the…

Let $ (T(t))_{t\geq0} $ be a positive $C_{0}$-semigroup with generator $A$ on a C$^*$-algebra or on the predual of a W$^*$-algebra. Then the growth bound $\omega_{0}$ equals $s(A)$. If the spectrum of $A$ is not empty, then $s(A)$, the…

Infinitesimal moments associated with infinitesimal freeness and infinitesimal conditional freeness are studied. For free random variables, we consider continuous deformations of moment functionals associated with Motzkin paths $w$, which…

In analogy with the construction of representations of adelic groups as restricted products of representations of local groups, we study restricted tensor products of Hilbert C*-modules and of C*-correspondences. The construction produces…

We prove a noncommutative $(p,p)$-Poincar\'e inequality for trace-symmetric quantum Markov semigroups on tracial von Neumann algebras, assuming only the existence of a spectral gap. Extending semi-commutative results of Huang and Tropp, our…

We prove that the Kadison-Kastler and Christensen distances are stable under the Banach space injective tensor product (resp., the Banach space projective tensor product) of a Banach space with any unital commutative $C^*$-algebra (resp.,…

In this paper, we show that the lattice of C*-covers of a non-selfadjoint operator algebra is either one point or uncountable. We prove that there are non-selfadjoint operator algebras with a one-point lattice in two ways: as an explicit…