Related papers: Dixmier Traces as Singular Symmetric Functionals a…

We prove that uniformly disconnected subsets of metric measure spaces with controlled geometry (complete, Ahlfors regular, supporting a Poincare inequality, and a mild topological condition) are contained in a quasisymmetric arc. This…

We characterise the normal trace space associated to extended (measure-valued) divergence-measure fields on the boundary of a set $E \subset \mathbb R^n$, as the Arens-Eells space $\mathrm{AE}(\partial E)$. Such a trace operator is…

We derive a formula for the regularized trace of operators with compact spectrum which act on the space of square integrable functions on the quotient of a semisimple Liegroup of real rank one by a convex-cocompact subgroup. The sum of…

For any densely defined, lower semi-continuous trace \tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2,…

Lichnerowicz's algebra of differential geometric operators acting on symmetric tensors can be obtained from generalized geodesic motion of an observer carrying a complex tangent vector. This relation is based upon quantizing the classical…

It is shown that a unital C*-algebra A has the Dixmier property if and only if it is weakly central and satisfies certain tracial conditions. This generalises the Haagerup-Zsido theorem for simple C*-algebras. We also study a uniform…

The Bishop property ($\symbishop$), introduced recently by K.P. Hart, T. Kochanek and the first-named author, was motivated by Pe{\l}czy{\'n}ski's classical work on weakly compact operators on $C(K)$-spaces. This property asserts that…

Commutators of bilinear Calder\'on-Zygmund operators and multiplication by functions in a certain subspace of the space of functions of bounded mean oscillations are shown to be compact on appropriate products of weighted Lebesgue spaces.

In this research article, we establish some identities and estimates for the operator norms and the Hausdorff measures of noncompactness of certain operators on some lacunary difference sequence spaces defined by Orlicz function. Moreover,…

In the present study, we establish both pointwise and uniform convergence in the space of logarithmically uniformly continuous and bounded functions for the max-product and max-min Durrmeyer-type exponential sampling operators. Furthermore,…

We consider discrete one-dimensional Schr\"odinger operators with quasi-Sturmian potentials. We present a new approach to the trace map dynamical system which is independent of the initial conditions and establish a characterization of the…

We examine the ranks of operators in semi-finite C*-algebras as measured by their densely defined lower semicontinuous traces. We first prove that a unital simple C*-algebra whose extreme tracial boundary is nonempty and finite contains…

Let M be a closed manifold. We show that the Kontsevich-Vishik trace, which is defined on the set of all classical pseudodifferential operators on M, whose (complex) order is not an integer greater than or equal to -dim M, is the unique…

In this work, firstly all normal extensions of a multipoint minimal operator generated by linear multipoint diferential-operator expression for first order in the Hilbert space of vector functions in terms of boundary values at the…

The celebrated Bishop theorem states that an operator is subnormal if and only if it is the strong limit of a net (or a sequence) of normal operators. By the Agler-Stankus theorem, $2$-isometries behave similarly to subnormal operator in…

We refine Epstein's method to prove joint concavity/convexity of matrix trace functions of Lieb type $\mathrm{Tr}\,f(\Phi(A^p)^{1/2}\Psi(B^q)\Phi(A^p)^{1/2})$ and symmetric (anti-) norm functions of the form…

Given a pair $(M,X)$, where $X$ is a smooth submanifold in a closed smooth manifold $M$, we study the operation, which takes each operator $D$ on the ambient manifold to a certain operator on the submanifold. The latter operator is called…

Using a global symbol calculus for pseudodifferential operators on tori, we build a canonical trace on classical pseudodifferential operators on noncommutative tori in terms of a canonical discrete sum on the underlying toroidal symbols. We…

The paper contains a description of the maximal ideal spaces (spectra) $\cM_A$ of bi-invariant function algebras $A$ on a compact group $G$. There are natural compatible structures in $\cM_A$: it is a compact topological semigroup with…

This paper investigates the recent Connes-Consani-Moscovici $D_{\log}^{(\lambda, N)}$ operators, whose spectra are currently hypothesized to approach the zeros of $\zeta\left(\frac{1}{2} +is\right)$ as $\lambda, N \rightarrow \infty$. It…