Related papers: Stable Elements and Property (S)

Inspired by the classical category theorems of Halmos and Rohlin for the discrete measure preserving transformations, we prove analogous results in the abstract setting of unitary and isometric C_0-semigroups on a separable Hilbert space.…

This paper has three parts. First, we study and characterize amenable and extremely amenable topological semigroups in terms of invariant measures using integral logic. We prove definability of some properties of a topological semigroup…

We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…

For a field K, rational function phi in K(z) of degree at least two, and alpha in P^1(K), we study the polynomials in K[z] whose roots are given by the solutions to phi^n(z) = alpha, where phi^n denotes the nth iterate of phi. When the…

Using a m\'elange of techniques at the rich intersection of deformation/rigidity theory, finite index subfactor theory, and geometric group theory, we prove the existence of a continuum of property (T) factors that are pairwise non-stably…

We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…

We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex cocompact subgroups of both mapping class groups and outer…

Given an action by a finite quantum group $\mathbb{G}$ on a von Neumann algebra $M$, we prove that a number of familiar $W^*$ properties are equivalent for $M$ and the fixed-point algebra $M^{\mathbb{G}}$ (i.e. hold or not simultaneously…

The Hecke algebras $\mathcal{H}_{n,k}$ of the group pairs $(S_{kn}, S_k\wr S_n)$ can be endowed with a filtration with respect to the orbit structures of the elements of $S_{kn}$ relative to the action of $S_{kn}$ on the set of…

The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes…

Finite elements, which are well-known and studied in the framework of vector lattices, are investigated in $\ell$-algebras, preferably in $f$-algebras, and in product algebras. The additional structure of an associative multiplication leads…

In this short \'etude, we observe that the full structure of a recollement on a stable infinity-category can be reconstructed from minimal data: that of a reflective and coreflective full subcategory. The situation has more symmetry than…

Let $R$ be a commutative noetherian ring, and $\mathcal{Z}$ a stable under specialization subset of $\Spec(R)$. We introduce a notion of $\mathcal{Z}$-cofiniteness and study its main properties. In the case $\dim(\mathcal{Z})\leq 1$, or…

We introduce a strong notion of quasiconvexity in finitely generated groups, which we call stability. Stability agrees with quasiconvexity in hyperbolic groups and is preserved under quasi-isometry for finitely generated groups. We show…

We study the spaces of polynomials stratified into the sets of polynomial with fixed number of roots inside certain semialgebraic region $\Omega$, on its border, and at the complement to its closure. Presented approach is a generalisation,…

Let $A$ be a simple C*-algebra of stable rank one and let $p$ and $q$ be two $\sigma$-compact open projections. It is proved that there is a continuous path of unitaries in ${\tilde A}$ which connects open sub-projections of $p$ which is…

In this paper, we study the Hilbert$-$Schmidt frame (HS-frame) theory for separable Hilbert spaces. We first present some characterizations of HS-frames and prove that HS-frames share many important properties with frames. Then, we show how…

We establish a crossed product decomposition theorem for stabilized Cuntz--Pimsner algebras. This result extends Cuntz's classical decomposition for the Cuntz algebras $\mathcal{O}_n$ and reveals an implicit symmetric structure within…

Return words are a classical tool for studying shift spaces with low factor complexity. In recent years, their projection inside groups have attracted some attention, for instance in the context of dendric shift spaces, of generation of…

Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older continuity of the associated Markov semigroups are discussed in some…