Related papers: Dixmier traces generated by exponentiation invaria…
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of…
We obtain a simple formula for the first-order trace of a regular differential operator on a segment perturbated by a multiplication operator. The main analytic ingredient of the proof is an improvement of the Tamarkin equiconvergence…
In this paper, we present a concise development of the well-studied theory of trace class operators on infinite dimensional (separable) Hilbert spaces suitable for an advanced undergraduate, as well as a construction of the inverse…
In this paper we study stable finiteness of ample groupoid algebras with applications to inverse semigroup algebras and Leavitt path algebras, recovering old results and proving some new ones. In addition, we develop a theory of (faithful)…
We introduce new entanglement measures on the set of density operators on tensor product Hilbert spaces. These measures are based on the greatest cross norm on the tensor product of the sets of trace class operators on Hilbert space. We…
Starting with a transient irreducible diffusion process $X^0$ on a locally compact separable metric space $(D, d)$, one can construct a canonical symmetric reflected diffusion process $\bar X$ on a completion $D^*$ of $(D, d)$ through the…
Traces of inverse powers of a positive definite symmetric tridiagonal matrix give lower bounds of the minimal singular value of an upper bidiagonal matrix. In a preceding work, a formula for the traces which gives the diagonal entries of…
We show that in $\text{O}(D)$ invariant matrix theories containing a large number $D$ of complex or Hermitian matrices, one can define a $D\rightarrow\infty$ limit for which the sum over planar diagrams truncates to a tractable, yet…
Two trace formulas for the spectra of arbitrary Hermitian matrices are derived by transforming the given Hermitian matrix $H$ to a unitary analogue. In the first type the unitary matrix is $e^{i(\lambda\II - H)}$ where $\lambda$ is the…
We investigate geometric properties of a class of trace functions expressed in terms of the deformed logarithmic and exponential functions. These trace functions and their properties may be of independent interest. We use them in particular…
About 20 years ago, J-P.~Serre announced a bound on the trace of elements of compact Lie groups under the adjoint representation together with related results, provided indications of his proofs, and invited a better proof. This note…
We compute explicitly traces of the Dirichlet form related to the Bessel process with respect to discrete measures as well as measures of mixed type. Then some global properties of the obtained Dirichlet forms, such as conservativeness,…
We prove that every surjective isometry between the unit spheres of two trace class spaces admits a unique extension to a surjective complex linear or conjugate linear isometry between the spaces. This provides a positive solution to…
Computing $\log\det(A)$ for large symmetric positive definite matrices arises in Gaussian process inference and Bayesian model comparison. Standard methods combine matrix-vector products with polynomial approximations. We study a different…
Given a finite tensor category $\mathcal{C}$, we prove that a modified trace on the tensor ideal of projective objects can be obtained from a suitable trivialization of the Nakayama functor as right $\mathcal{C}$-module functor. Using a…
We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…
We generalise the result of Berger and Shaw the trace formula for Hardy Hilbert space to a larger class of rotation invariant Hilbert function spaces on the unit disk. We also demonstrate many meaningful examples of these Hilbert spaces by…
Motivated by the "composition theorems" of Chernikov-Hempel and Abd Aldaim-Conant-Terry we introduce $k$-trace definability between first order theories. Any theory which is $k$-trace definable in a NIP theory is $k$-NIP and any theory…
Given a graded sequence of ideals (a_m) on a smooth variety $X$ having finite log canonical threshold, suppose that for every m we have a divisor E_m over X that computes the log canonical threshold of a_m, and such that the log…
We study algebraic K-theory and topological Hochschild homology in the setting of bimodules over a stable category, a datum we refer to as a laced category. We show that in this setting both K-theory and THH carry universal properties, the…