Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2107.03687

Multiple operator integrals in non-separable von Neumann algebras

Evangelos A. Nikitopoulos
View original source ↗Read source document ↗Export metadata ↓

Abstract

A multiple operator integral (MOI) is an indispensable tool in several branches of noncommutative analysis. However, there are substantial technical issues with the existing literature on the "separation of variables" approach to defining MOIs, especially when the underlying Hilbert spaces are not separable. In this paper, we provide a detailed development of this approach in a very general setting that resolves existing technical issues. Along the way, we characterize several kinds of "weak" operator valued integrals in terms of easily checkable conditions and prove a useful Minkowski-type integral inequality for maps with values in a semifinite von Neumann algebra.

Explore related subjects

math.OAmath.FA

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Evangelos A. Nikitopoulos. 2023-12-23. Multiple operator integrals in non-separable von Neumann algebras. https://doi.org/10.7900/jot.2021aug19.2357

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↗