Related papers: Finite sections of band-dominated operators on dis…

We consider spatial discretizations by the finite section method of the restricted group algebra of a finitely generated discrete group, which is represented as a concrete operator algebra via its left-regular representation. Special…

An operator on an $l^{p}$-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. It is known that a rich band-dominated operator is $\mathcal{P}$-Fredholm (which is…

Let $(\cX, \rho)$ be a discrete metric space. We suppose that the group $\sZ^n$ acts freely on $X$ and that the number of orbits of $X$ with respect to this action is finite. Then we call $X$ a $\sZ^n$-periodic discrete metric space. We…

We establish necessary and sufficient conditions for the stability of the finite section method for operators belonging to a certain $C^*$-algebra of operators acting on the Hilbert space $l^2_H(\mathbb{Z})$ of $H$-valued sequences where…

This paper presents the Fredholm theory on l^p-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p=\infty…

In this paper we study the semi-Fredholm property of band-dominated operators $A$ and prove that it already implies the Fredholmness of $A$ in all cases where this is not disqualified by obvious reasons. Moreover, this observation is…

An operator $A$ on an $l^p$-space is called band-dominated if it can be approximated, in the operator norm, by operators with a banded matrix representation. The coset of $A$ in the Calkin algebra determines, for example, the Fredholmness…

Suppose $\Gamma$ is a Carleson Jordan curve with logarithmic whirl points, $\varrho$ is a Khvedelidze weight, $p:\Gamma\to(1,\infty)$ is a continuous function satisfying $|p(\tau)-p(t)|\le -\mathrm{const}/\log|\tau-t|$ for $|\tau-t|\le…

We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth, compact, manifold $M$ without boundary and let…

We study band-dominated operators on (subspaces of) $L_p$-spaces over metric measure spaces of bounded geometry satisfying an additional property. We single out core assumptions to obtain, in an abstract setting, definitions of limit…

The main aim of the paper is Fredholm properties of a class of bounded linear operators acting on weighted Lebesgue spaces on an infinite metric graph $\Gamma$ which is periodic with respect to the action of the group ${\mathbb Z}^n$. The…

We consider sequences of finitely generated discrete subgroups Gamma_i=rho_i(Gamma) of a rank 1 Lie group G, where the representations rho_i are not necessarily faithful. We show that, for algebraically convergent sequences (Gamma_i),…

In this paper, we prove the existence of a particular diagonalization for normal bounded operators defined on subspaces of $L^2(\mathfrak{S})$ where $\mathfrak{S}$ is a second countable LCA group. The subspaces where the operators act are…

The aim of this note is to generalize the notion of Fredholm operator to an arbitrary $C^*$-algebra. Namely, we define "finite type" elements in an axiomatic way, and also we define Fredholm type element $a$ as such element of a given…

We study, to certain Banach spaces $X$, families of weighted composition operators. Notably, we show that if this family form a strongly continuous semigroup, then its infinitesimal generator ($\Gamma, D(\Gamma)$) is given by $\Gamma f =…

For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\to L^2(G)$ is called convolution dominated if there exists $a\in L^1(G)$ such that for all $f \in…

Withdrawn due to a likely error with the homeomorphism at line (4). Old abstract: In the monograph 'Limit Operators and their Applications in Operator Theory', the authors define the operator spectrum of a band-dominated operator T and…

By relating notions from quantum harmonic analysis and band-dominated operator theory, we prove that over any locally compact abelian group $G$, the operator algebra $\mathcal C_1$ from quantum harmonic analysis agrees with the intersection…

We establish a necessary and sufficient criterion for the Fredholmness of a general locally compact band-dominated operator $A$ on $L^p(R)$ and solve the long-standing problem of computing its Fredholm index in terms of the limit operators…

We study the essential spectrum and Fredholm properties of integral and pseudodiferential operators associated to (maybe non-commutative) locally compact groups G. The techniques involve crossed product C*-algebras. We extend previous…