Related papers: A note on two Conjectures on Dimension funcitons o…

A simple Steinberg algebra associated to an ample Hausdorff groupoid $G$ is algebraically purely infinite if and only if the characteristic functions of compact open subsets of the unit space are infinite idempotents. If a simple Steinberg…

Recently Conrey, Farmer and Zirnbauer conjectured formulas for the averages over a family of ratios of products of shifted L-functions. Their L-functions Ratios Conjecture predicts both the main and lower order terms for many problems,…

The completion $\overline{A}[\tau]$ of a locally convex *-algebra $A [ \tau ]$ with not jointly continuous multiplication is a *-vector space with partial multiplication $xy$ defined only for $x$ or $y \in A_{0}$, and it is called a…

Using different descriptions of the Cuntz semigroup and of the Pedersen ideal, it is shown that $\sigma$-unital simple $C^*$-algebras with almost unperforated Cuntz semigroup, a unique lower semicontinuous $2$-quasitrace and whose…

We investigate how a C*-algebra could consist of functions on a noncommutative set: a discretization of a C*-algebra $A$ is a $*$-homomorphism $A \to M$ that factors through the canonical inclusion $C(X) \subseteq \ell^\infty(X)$ when…

The existence of a well-behaved dimension of a finite von Neumann algebra (see [19]) has lead to the study of such a dimension of finite Baer *-rings (see [26]) that satisfy certain *-ring axioms (used in [9]). This dimension is closely…

We shall introduce the approximate representability and the Rohlin property for coactions of a finite dimensional $C^*$-Hopf algebra on a unital $C^*$-algebra and discuss some basic properties of approximately representable coactions and…

Foulkes' conjecture has several generalisations due to Doran, Abdesselam--Chipalkatti, Bergeron, and Troyka. For the special linear Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, these assert that given $a \le c \le d \le b$ with $ab=cd$, the…

The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of…

Let \(Q \subseteq \mathbb{N}\) be a subset, and let \(\psi\colon \mathbb{N} \to [0, \tfrac{1}{2})\), \(\theta\colon \mathbb{N} \to \mathbb{R}\) be functions. Let \(\{A_q\}\) and \(\{B_q\}\) be sequences of integers such that \(\gcd(A_q,…

Let $X$ be a smooth projective variety over an algebraically closed field of arbitrary characteristic, and $f$ a dynamical correspondence of $X$. In 2016, the second author conjectured that the dynamical degrees of $f$ defined by the…

A C*-algebra is n-homogeneous (where n is finite) if every its nonzero irreducible representation acts on an n-dimensional Hilbert space. An elementary proof of Fell's characterization of n-homogeneous C*-algebras (by means of their…

We study $C^*$-algebras generated by Toeplitz operators acting on the standard weighted Bergman space $\mathcal{A}_{\lambda}^2(\mathbb{B}^n)$ over the unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$. The symbols $f_{ac}$ of generating operators…

We study the $1$-level density of low-lying zeros of Dirichlet $L$-functions in the family of all characters modulo $q$, with $Q/2 < q\leq Q$. For test functions whose Fourier transform is supported in $(-3/2, 3/2)$, we calculate this…

By Glimm's dichotomy, a separable, simple $\textrm{C}^*$-algebra has continuum-many unitarily inequivalent irreducible representations if, and only if, it is non-type I while all of its irreducible representations are unitarily equivalent…

In the present paper we prove a duality theory for compact groups in the case when the C*-algebra A, the fixed point algebra of the corresponding Hilbert C*-system (F,G), has a nontrivial center Z and the relative commutant satisfies the…

We show that the following conditions on a C*-algebra are equivalent: (i) it has the fixed point property for nonexpansive mappings, (ii) the spectrum of every self adjoint element is finite, (iii) it is finite dimensional. We prove that…

We show that every unital amenable separable simple $C^*$-algebra with finite tracial rank which satisfies the UCT has in fact tracial rank at most one. We also show that unital separable simple $C^*$-algebrass which are "tracially" locally…

We remove the assumption of the continuum hypothesis from the Akemann-Doner construction of a non-separable $C^*$-algebra $A$ with only separable commutative $C^*$-subalgebras. We also extend a result of Farah and Wofsey's, constructing…

In the recent paper \cite{SER}, the second author proved a divergence-quasiconcavity inequality for the following functional $ \mathbb{D}(A)=\int_{\mathbb{T}^n} det(A(x))^{\frac{1}{n-1}}\,dx$ defined on the space of $p$-summable positive…