Related papers: Essential normality, essential norms and hyperrigi…

Given a braided tensor *-category C with conjugate (dual) objects and irreducible unit together with a full symmetric subcategory S we define a crossed product C\rtimes S. This construction yields a tensor *-category with conjugates and an…

The variance conjecture in Asymptotic Convex Geometry stipulates that the Euclidean norm of a random vector uniformly distributed in a (properly normalised) high-dimensional convex body $K\subset {\mathbb R}^n$ satisfies a Poincar\'e-type…

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras.…

On a (pseudo-)Riemannian manifold (M,g), some fields of endomorphisms i.e. sections of End(TM) may be parallel for g. They form an associative algebra A, which is also the commutant of the holonomy group of g. As any associative algebra, A…

In this paper, we establish $C^{1, \alpha}$ regularity upto the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. Our main result Theorem 2.1 constitutes the boundary analogue of the…

We give a simple sufficient condition for a spun-normal surface in an ideal triangulation to be incompressible, namely that it is a vertex surface with non-empty boundary which has a quadrilateral in each tetrahedron. While this condition…

Let $R$ be a reduced affine $\mathbb C$-algebra, with corresponding affine algebraic set $X$. Let $\mathcal C(X)$ be the ring of continuous (Euclidean topology) $\mathbb C$-valued functions on $X$. Brenner defined the \emph{continuous…

Let $G$ be a simple graph on $n$ vertices and $J_G$ denote the corresponding binomial edge ideal in $S = K[x_1, \ldots, x_n, y_1,\ldots, y_n].$ We prove that the Castelnuovo-Mumford regularity of $J_G$ is bounded above by $c(G)+1$ when $G$…

It is known that the fundamental group homomorphism $\pi_1(T^2) \to \pi_1(S^3\setminus K)$ induced by the inclusion of the boundary torus into the complement of a knot $K$ in $S^3$ is a complete knot invariant. Many classical invariants of…

A result due to Williams, Stampfli and Fillmore shows that an essential isometry $T$ on a Hilbert space $\mathcal{H}$ is a compact perturbation of an isometry if and only if ind$(T)\le 0$. A recent result of S. Chavan yields an analogous…

We introduce a unified geometric framework for domains satisfying a geometric normal property (C-GNP) relative to a strictly convex set \(C\). Under the fundamental assumption that the source \(f\) is supported within the core \(C\), we…

We consider inductive systems of C*-algebras with completely positive contractive connecting maps. We define a condition, called C*-encoding, which is sufficient for the limit of the system to be completely order isomorphic to a C*-algebra…

We introduce and investigate a class of ring ideals, termed ring $\mathrm{M}$-ideals, inspired by the Alfsen--Effros theory of $\mathrm{M}$-ideals in Banach spaces. We show that $\mathrm{M}$-ideals extend the classical notion of essential…

We give a characterization of extremal irreducible discrete subfactors $(N\subseteq M, E)$ where $N$ is type ${\rm II}_1$ in terms of connected W*-algebra objects in rigid C*-tensor categories. We prove an equivalence of categories where…

This paper introduces a canonical Polish groupoid associated to any separable unital C*-algebra, termed the unitary conjugation groupoid. It is defined as the semidirect product of the algebra's dual space by its unitary group, acting by…

We prove topological regularity results for isoperimetric sets in PI spaces having a suitable deformation property, which prescribes a control on the increment of the perimeter of sets under perturbations with balls. More precisely, we…

Let $M$ be Hadamard manifold with sectional curvature $K_{M}\leq-k^{2}$, $k>0$. Denote by $\partial_{\infty}M$ the asymptotic boundary of $M$. We say that $M$ satisfies the strict convexity condition (SC condition) if, given…

We prove that the regular von Neumann subalgebras $B$ of the hyperfinite II_1 factor $R$ satisfying the condition $B'\cap R=Z(B)$ are completely classified (up to conjugacy by an automorphism of $R$) by the associated discrete measured…

To every one-sided shift space $\mathsf{X}$ we associate a cover $\tilde{\mathsf{X}}$, a groupoid $\mathcal{G}_{\mathsf{X}}$ and a $\mathrm{C^*}$-algebra $\mathcal{O}_{\mathsf{X}}$. We characterize one-sided conjugacy, eventual conjugacy…

For a smooth, non-degenerate locally integrable structure of hypersurface type on a manifold $M$, we provide necessary and sufficient conditions for it to be equivalent, near a point, to a real-analytic locally integrable structure (the…