Related papers: Trace operators on Wiener amalgam spaces
In \cite{g5}, we defined and investigated the grand Wiener amalgam space $W(L^{p),\theta_1}(\Omega), L^{q),\theta_2}(\Omega))$ , where $1<p,q<\infty, \theta_1>0, \theta_2>0$, $\Omega\subset\mathbb R^{n} $ and the Lebesgue measure of…
This article - a part of a multipaper project investigating arithmetic mean ideals - investigates the codimension of commutator spaces [I, B(H)] of operator ideals on a separable Hilbert space, i.e., ``How many traces can an ideal support?"…
We study several trace operators and spaces that are related to the bi-Laplacian. They are motivated by the development of ultraweak formulations for the bi-Laplace equation with homogeneous Dirichlet condition, but are also relevant to…
We prove trace identities for commutators of operators, which are used to derive sum rules and sharp universal bounds for the eigenvalues of periodic Schroedinger operators and Schroedinger operators on immersed manifolds. In particular, we…
This research investigates the relations between the fixed points of asymptotically contractive operators defined on complete liner metric spaces, in general, and in separable Hilbert spaces in particular and their obtained truncations of…
We consider functions of multi-dimensional versions of truncated Wiener--Hopf operators with smooth symbols, and study the scaling asymptotics of their traces. The obtained results extend the asymptotic formulas obtained by H. Widom in the…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
We prove a Duistermaat-Guillemin trace formula for transversally elliptic operators on a compact foliated manifold.
We obtain general theorems which enable the calculation of the Dixmier trace in terms of the asymptotics of the zeta function and of the heat operator in a general semi-finite von Neumann algebra. Our results have several applications. We…
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial $W^*$-probability space. More precisely, we consider operator-valued Wigner and Wishart matrices and prove quantitative convergence to…
We present other examples illustrating the operator-theoretic approach to invariant integrals on quantum homogeneous spaces developed by Kuersten and the second author. The quantum spaces are chosen such that their coordinate algebras do…
We consider Schr\"odinger operators with complex-valued decreasing potentials on the half-line. Such operator has essential spectrum on the half-line plus eigenvalues (counted with algebraic multiplicity) in the complex plane without the…
We consider Schr\"odinger operators with periodic magnetic and electric potentials on periodic discrete graphs. The spectrum of such operators consists of a finite number of bands. We determine trace formulas for the magnetic Schr\"odinger…
This paper presents some relations for orthonormal bases in the Minkowski space and isotropic tetrads constructed from the vectors of these bases. As an example of an application of the obtained formulae, in particular recursion relations,…
In this paper we study ergodicity and mixing property of some measure preserving transformations on the Wiener space (W,H,\mu) which are generated by some random unitary operators defined on the Cameron-Martin space H.
Let $\mathcal{M}$ be an atomless semifinite von Neumann algebra (or an atomic von Neumann algebra with all atoms having the same trace) acting on a (not necessarily separable) Hilbert space $H$ equipped with a semifinite faithful normal…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Properties of compositions and convex combinations of averaged nonexpansive operators are investigated and applied to the design of new fixed point algorithms in Hilbert spaces. An extended version of the forward-backward splitting…
Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…
We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…