Related papers: Higher-Order Trace Formulas for Contractive and Di…

We establish sharp trace- and Korn-type inequalities that involve vectorial differential operators, the focus being on situations where global singular integral estimates are not available. Starting from a novel approach to sharp Besov…

The trace formula for the evolution operator associated with nonlinear stochastic flows with weak additive noise is cast in the path integral formalism. We integrate over the neighborhood of a given saddlepoint exactly by means of a smooth…

Given $H$ self-adjoint, $V$ symmetric and relatively $H$-bounded, and $f:\mathbb{R}\to\mathbb{C}$ satisfying mild conditions, we show that the Gateaux derivative $$\frac{d^n}{dt^n}f(H+tV)|_{t=0}$$ exists in the operator norm topology, for…

We study extended zeta-function residues on principal ideals of compact operators and their connections with Dixmier traces. We establish a Lidskii-type formula for continuous singular traces on these ideals. Using this formula, we obtain a…

We define Schatten classes of adjointable operators on Hilbert modules over abelian $C^*$-algebras. Many key features carry over from the Hilbert space case. In particular, the Schatten classes form two-sided ideals of compact operators and…

One of the long standing questions in the theory of Schatten-von Neumann ideals of compact operators is whether their norms have the same differentiability properties as the norms of their commutative counterparts. We answer this question…

We study integral operators on the space of square-integrable functions from a compact set, $X$, to a separable Hilbert space, $H$. The kernel of such an operator takes values in the ideal of Hilbert-Schmidt operators on $H$. We establish…

In this work we study Schatten-von Neumann classes of tensor products of invariant operators on Hilbert spaces. In the first part we first deduce some spectral properties for tensors of anharmonic oscillators thanks to the knowledge on…

We consider functions $f(T,R)$ of pairs of noncommuting contractions on Hilbert space and study the problem for which functions $f$ we have Lipschitz type estimates in Schatten--von Neumann norms. We prove that if $f$ belongs to the Besov…

In this paper we prove that for an arbitrary pair $\{T_1,T_0\}$ of contractions on Hilbert space with trace class difference, there exists a function $\boldsymbol\xi$ in $L^1({\Bbb T})$ (called a spectral shift function for the pair…

For a pair $(A,B)$ of not necessarily bounded and not necessarily commuting self-adjoint operators and for a function $f$ on the Euclidean space ${\Bbb R}^2$ that belongs to the inhomogeneous Besov class $B_{\infty,1}^1({\Bbb R}^2)$, we…

We construct a new example of the high derivative four-dimensional conformal operator. This operator acts on fermions, and its contribution to the trace anomaly has opposite sign, as compared to conventional scalars, spinors and vectors.…

We derive trace formulas of the Buslaev-Faddeev type for quantum star graphs. One of the new ingredients is high energy asymptotics of the perturbation determinant.

Given integers $m$, $n$ and $k$, we give an explicit formula with an optimal error term (with square root cancelation) for the Petersson trace formula involving the $m$-th and $n$-th Fourier coefficients of an orthonormal basis of…

We investigate the spectral asymptotic behavior of operator-valued classical pseudo-differential operators ($\Psi$DOs) for negative order with symbols taking values in a semifinite von Neumann algebran $\mathcal{M}$ equipped with a normal…

We provide criteria for self-adjointness and {\tau}-Fredhomness of first and second order differential operators acting on sections of infinite dimensional bundles, whose fibers are modules of finite type over a von Neumann algebra A…

Dykema, Sukochev and Zanin used a Peano curve covering the support of the Brown measure of an operator T in a diffuse, finite von Neumann algebra to give an ordering to the support of the Brown measure, and create a decomposition T = N + Q,…

First-order differential operators arising from the representation-theoretic decomposition of the covariant derivative play a central role in Riemannian geometry. In this paper, we study Stein-Weiss $O(n)$-gradients acting on covariant…

In this paper we introduce and study pseudo-differential operators with operator valued symbols on the abstract Heisenberg group $\mathbb{H}(G):=G \times \widehat{G} \times \mathbb{T},$ where $G$ a locally compact abelian group with its…

The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two…