Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.30083

Joint Uniform Continuity of Reduced Free Products for strong convergence

Ben Hayes
View original source ↗Read source document ↗Export metadata ↓

Abstract

We investigate a generalization of Skoufranis' theorem on joint continuity of free products of laws in the strong topology. Namely, we show that this operation is moreover \emph{uniformly continuous}. Our methods follows those of Piser and go through the estimates of Ricard-Xu.

Explore related subjects

math.OAmath.FA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ben Hayes. 2026-10-21. Joint Uniform Continuity of Reduced Free Products for strong convergence. https://arxiv.org/abs/2610.30083

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Noncommutative principal bundles and central extensions

Motivated by the classical theory of spin structures, we develop a theory for lifting free C$^*$-dynamical systems, a.k.a. noncommutative principal bundles, along central extensions. This theory extends the bundle-theoretic notion of spin structures and yields a complete existence and classification result for such lifts. Using factor system techniques and Picard formalism, our approach introduces new invariants and obstruction classes, thereby unifying geometric, cohomological, and operator-algebraic perspectives. A range of examples demonstrates the scope of the theory.

math.OA↗
arXiv2026

Aperiodic automorphisms of the Razak--Jacelon algebra

We completely classify aperiodic automorphisms of the Razak--Jacelon algebra $\mathcal{W}$ up to outer conjugacy. As a technical ingredient, based on the works of Connes, Herman--Ocneanu, Kishimoto, and Sato, we introduce a notion of weak stability for automorphisms of simple separable monotracial C$^*$-algebras. We also consider automorphisms of UHF algebras of infinite type and the Jiang--Su algebra. In particular, we classify aperiodic ``UHF-absorbing'' automorphisms of UHF algebras of infinite type up to outer conjugacy.

math.OA↗
arXiv2026

Characterisations for coarse embeddability via quasi-locality and Schur multipliers

We establish three new characterisations of coarse embeddability into Hilbert space for discrete metric spaces of bounded geometry in terms of escaping quasi-local couplings, Schur multipliers, and operator norm state localisation. As applications, we prove that if a sparse metric space of bounded geometry is coarsely embeddable into Hilbert space, then every ghost projection in the quasi-local algebra is compact, while we also provide a counterexample to the converse implication. Finally, we characterise coarse embeddability into Hilbert space via the relative Haagerup property for the quasi-local algebra, and investigate its relation to coarse embeddability into $\ell^p$ for $p>2$.

math.OA↗