Related papers: Spectral finiteness, quantum norm continuity and c…
The spectrum $\omega(G)$ of a finite group $G$ is the set of element orders of $G$. Finite groups $G$ and $H$ are isospectral if their spectra coincide. Suppose that $L$ is a simple classical group of sufficiently large dimension (the lower…
A group $\Gamma$ is said to be uniformly HS stable if any map $\varphi : \Gamma \to U(n)$ that is almost a unitary representation (w.r.t. the Hilbert Schmidt norm) is close to a genuine unitary representation of the same dimension. We…
We consider a quantum particle in a periodic structure submitted to a constant external electromotive force. The periodic background is given by a smooth potential plus singular point interactions and has the property that the gaps between…
The Hilbert space $\mathcal H$ of backward renormalisation of an anyonic quantum spin chain affords a unitary representation of Thompson's group $F$ via local scale transformations. Given a vector in the canonical dense subspace of…
The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in…
We investigate questions of maximal symmetry in Banach spaces and the structure of certain bounded non-unitarisable groups on Hilbert space. In particular, we provide structural information about bounded groups with an essentially unique…
We establish a characterization of doubly power-bounded elements with finite spectrum in Banach algebras. In particular, we present a spectral decomposition for such elements, extending a classical theorem of Gelfand concerning doubly…
This survey aims to highlight some of the consequences that representable (and continuous) functionals have in the framework of Banach quasi *-algebras. In particular, we look at the link between the notions of *-semisimplicity and full…
We analyze the spectral properties of a particular class of unbounded open sets. These are made of a central bounded ``core'', with finitely many unbounded tubes attached to it. We adopt an elementary and purely variational point of view,…
The spectrum of a finite group is the set of orders of its elements. We are concerned with finite groups having the same spectrum as a direct product of nonabelian simple groups with abelian Sylow $2$-subgroups. For every positive integer…
We define solvable quantum mechanical systems on a Hilbert space spanned by bipartite ribbon graphs with a fixed number of edges. The Hilbert space is also an associative algebra, where the product is derived from permutation group…
We show that a compact representation of a semisimple Lie group has an orthogonal decomposition into finite length representations. This generalises and simplifies a number of more special spectral theorems in the literature. We apply it to…
This paper explores the interactions of absolute continuity of the (quasi)norm with the concepts that are fundamental in the theory of rearrangement-invariant (quasi-)Banach function spaces, such as the Luxemburg representation or the…
A class of quantum analogues of compact symmetric spaces of classical type is introduced by means of constant solutions to the reflection equations. Their zonal spherical functions are discussed in connection with $q$-orthogonal…
For finite-dimensional linear semigroups which leave a proper cone invariant it is shown that irreducibility with respect to the cone implies the existence of an extremal norm. In case the cone is simplicial a similar statement applies to…
The main purpose of this paper is to treat semigroups properties, like norm continuity, compactness and differentiability for perturbed semigroups in Banach spaces. In particular, we investigate three large classes of perturbations,…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…
We give a proof that in settings where Von Neumann deficiency indices are finite the spectral counting functions of two different self-adjoint extensions of the same symmetric operator differ by a uniformly bounded term (see also…
In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…