Related papers: When the algebraic difference of two central Canto…

We prove that separable C*-algebras which are completely close in a natural uniform sense have isomorphic Cuntz semigroups, continuing a line of research developed by Kadison - Kastler, Christensen, and Khoshkam. This result has several…

We are interested in a fragmentation process. We observe fragments frozen when their sizes are less than $\epsilon$ ($\epsilon$ > 0). Is is known ([BM05]) that the empirical measure of these fragments converges in law, under some…

We study differentiability of topological conjugacies between expanding piecewise $C^{1+\epsilon}$ interval maps. If these conjugacies are not $C^1$, then they have zero derivative almost everywhere. We obtain the result that in this case…

In this paper, we characterize $\ell$-open and $\ell$-closed $C^*$-algebras and deduce that $\ell$-open $C^*$-algebras are $\ell$-closed, as conjectured by Blackadar. Moreover, we show that a commutative unital $C^*$-algebra is $\ell$-open…

Using a slight modification of an argument of Croot, Ruzsa and Schoen we establish a quantitative result on the existence of a dilated copy of any given configuration of integer points in sparse difference sets. More precisely, given any…

It is shown that the Cuntz semigroup is a complete invariant for the C*-algebras that can be realized as an inductive limit of a sequence of finite direct sums of splitting interval algebras.

For a simple $C^*$-algebra $A$ and any other $C^*$-algebra $B$, it is proved that every closed ideal of $A \otimes^{\min} B$ is a product ideal if either $A$ is exact or $B$ is nuclear. Closed commutator of a closed ideal in a Banach…

The Abel differential equation $y'=p(x)y^3 + q(x) y^2$ with polynomial coefficients $p,q$ is said to have a center on $[a,b]$ if all its solutions, with the initial value $y(a)$ small enough, satisfy the condition $y(a)=y(b)$. The problem…

Given a Hausdorff compact space X, we study the C^*-(semi)-norms on the algebraic tensor product $A\otimes_{alg,C(X)} B$ of two C(X)-algebras A and B over C(X). In particular, if one of the two C(X)-algebras defines a continuous field of…

I prove two variants of the $ABC$ sum-product theorem for $\delta$-separated sets $A,B,C \subset [0,1]$ satisfying Katz-Tao spacing conditions. The main novelty is that the cardinality of the sets $B,C$ need not match their…

Let $x, y$ be two normal elements in a unital simple C*-algebra $A.$ We introduce a function $D_c(x, y)$ and show that in a unital simple AF-algebra there is a constant $1>C>0$ such that $$ C\cdot D_c(x, y)\le {\rm dist}({\cal U}(x),{\cal…

We study uniform perturbations of crossed product C$^*$-algebras by amenable groups. Given a unital inclusion of C$^*$-algebras $C\subseteq D$ and sufficiently close separable intermediate C$^*$-subalgebras $A$, $B$ for this inclusion with…

This paper systematically investigates the properties and characterization of interval B-tensors and interval double B-tensors. We propose verifiable necessary and sufficient conditions that allow for determining whether an entire interval…

We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a…

We build the first examples of diffeomorphisms that are distorted in a group of $C^r$ diffeomorphisms yet undistorted in the corresponding group of $C^s$ diffeomorphisms, where $r < s$. This explicit construction is performed for the closed…

Let $u:A\to B$ be a bounded linear operator between two $C^*$-algebras $A,B$. The following result was proved by the second author. Theorem 0.1. There is a numerical constant $K_1$ such that for all finite sequences $x_1,\ldots, x_n$ in $A$…

Motivated by [2] and [5], the notions of interior and exterior angles between a pair of compatible intermediate W*-subalgebras of an inclusion of W*-algebras with a normal conditional expectation with finite probabilistic index are…

We show that for all Cantor set $K_1$ on ${\mathbb R}^d$, it is always possible to find another Cantor set $K_2$ so that the sum $g(K_1)+ K_2$ (where $g$ is a $C^1$ local diffeomorphism) has non-empty interior, and the existence of the…

We say that an inclusion of an algebra $A$ into a $C^*$-algebra $B$ has the ideal separation property if closed ideals in $B$ can be recovered by their intersection with $A$. Such inclusions have attractive properties from the point of view…

We investigate the algebraic genericity of various families of continuous functions exhibiting extreme irregularity, focusing on fractal dimensions, H\"older regularity, and fractional differentiability. Our first main result shows that for…