Cédric Arhancet

activity

20092026

most citedNoncommutative Figa-Talamanca-Herz algebras for Schur multipliers

5 citations · 13 across the 35 of their papers we have counts for

collaborators

43 papers

math.FA2026

Radial Schur multipliers on trees and quantitative Fourier--Schur separation

Cédric Arhancet

We study ordinary and completely bounded norms of radial Schur multipliers on trees. On the homogeneous tree of countably infinite degree, we show that boundedness implies complete…

math.FA2026

A modular theory of contractive projections on Banach spaces with applications to noncommutative $L^{p}$ -spaces

Cédric Arhancet

We develop a differential-geometric approach to contractive projections on complex Banach spaces based on Levi forms of plurisubharmonic functions. We show that if a projection $P$ …

math.FA2026

Multiplicativity of the weak Haagerup constant

Cédric Arhancet

We prove that the weak Haagerup constant is multiplicative with respect to direct products, namely $Λ_{WH} (G \times H) = Λ_{WH} (G) Λ_{WH} (H)$ for any local…

math.FA2026

Optimal square size for separating the operator and completely bounded norms of Schur multipliers on $S^{4}$

Cédric Arhancet

We determine the smallest square size at which the operator norm and the completely bounded norm of a Schur multiplier on $S^{4}$ can differ. More precisely, for $A=\begin{bmatrix}1&…

math.FA2026

Completely isometric subspaces of noncommutative $L^{p}$ -spaces and contractive projections

Cédric Arhancet

We investigate the relation between the complete isometry class of subspaces of noncommutative $L^{p}$ -spaces and their contractive complementability, where $1 < p < \infty$ …

math.FA2026

Spectral nonassociative $L^{p}$ -spaces for $JBW^{*}$ -algebras

Cédric Arhancet

We complete the construction of tracial spectral nonassociative $L^{p}$ -spaces for general $JBW^{*}$ -algebras. More precisely, if $M$ is a $JBW^{*}$ -…

math.FA2026

A reverse Riesz estimate combined with a spectral gap implies a Poincaré inequality

Cédric Arhancet

Working at the level of a sectorial operator $A$ on a Banach space $X$ and an unbounded operator $\partial$ defined on a subspace of $X$ in another Banach space $Y$ , we show that a…

math.OA2026

Spectral versus interpolation norms in tracial nonassociative $L^{p}$ -spaces

Cédric Arhancet, Lei Li

We investigate the metric structure of nonassociative $L^{p}$ -spaces associated with tracial $JW^{*}$ -algebras. While noncommutative $L^{p}$ -spaces arising fro…

math.OA2026

On the convex structure of the space of quantum channels which act as Fourier multipliers

Cédric Arhancet, Lei Li

If $G$ is a compact group, continuous normalized positive definite functions are in one-to-one correspondence with unital quantum channels acting as Fourier multipliers on the grou…

math.FA2026

Dolbeault-Dirac operators on compact Kähler manifolds in Banach noncommutative geometry

Cédric Arhancet

We develop an $L^{p}$ -theory for Dolbeault-Dirac operators on compact Kähler manifolds with coefficients in a Hermitian holomorphic vector bundle $E$ . For each $p \in (1,\in…

math.FA2025

The $L^{p}$ -index of the Hodge-Dirac operator on compact Riemannian manifolds

Cédric Arhancet

We investigate the spectral and index-theoretic properties of the Hodge-Dirac operator $D = d + d^{*}$ acting on the Banach space $L^{p} (Ω^{∙} (M))$ of di…

math.FA2024★ 1 cited

Classical harmonic analysis viewed through the prism of noncommutative geometry

Cédric Arhancet

The aim of this paper is to bridge noncommutative geometry with classical harmonic analysis on Banach spaces, focusing primarily on both classical and noncommutative $L^{p}$ …

math.CA2024

Functional calculus and semilinear evolution equations for the Taibleson operator on non-Archimedean local fields

Cédric Arhancet, Christoph Kriegler

For any non-Archimedean local field $K$ and any integer $n \geq 1$ , we show that the Taibleson operator admits a bounded $H^{\infty} (Σ_{θ})$ functional calculus on th…

quant-ph2024

Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras

Cédric Arhancet

We investigate a new class of unital quantum channels on $M_{2^{k}}$ , acting as radial multipliers when we identify the matrix algebra $M_{2^{k}}$ with a finite-dimen…

math.FA2024

Curvature, Dolbeault-Dirac operators, and an $L^{p}$ -index theorem on compact Kähler manifolds

Cédric Arhancet

We develop an $L^{p}$ -Banach noncommutative-geometric framework for Dolbeault-Dirac operators on compact Kähler manifolds with coefficients in a Hermitian holomorphic vector…

math.FA2023★ 1 cited

The harmonic oscillator on the Moyal-Groenewold plane: an approach via Lie groups and twisted Weyl tuples

Cédric Arhancet, Lukas Hagedorn, Christoph Kriegler +1

This paper investigates the functional calculus of the harmonic oscillator on each Moyal-Groenewold plane, the noncommutative phase space which is a fundamental object in quantum m…

math.OA2023★ 1 cited

Nonassociative $L^{p}$ -spaces and embeddings in noncommutative $L^{p}$ -spaces

Cédric Arhancet

We define a notion of nonassociative $L^{p}$ -space associated to a $JBW^{*}$ -algebra (Jordan von Neumann algebra) equipped with a normal faithful state $φ$ . In the pa…

math.CA2023

Separating Fourier and Schur multipliers

Cédric Arhancet, Christoph Kriegler, Christian Le Merdy +1

Let $G$ be a locally compact unimodular group, let $1 \leq p < \infty$ ,let $ϕ \in L^{\infty} (G)$ and assume that the Fourier multiplier $M_{ϕ}$ associated with $ϕ$ is bounded on the noncomm…

math.OA2022

Spectral triples, Coulhon-Varopoulos dimension and heat kernel estimates

Cédric Arhancet

We investigate the relations between the (completely bounded) local Coulhon-Varopoulos dimension and the spectral dimension of spectral triples associated to sub-Markovian semigrou…

math.FA2022★ 1 cited

Decomposable Fourier Multipliers and an Operator-Algebraic Characterization of Amenability

Cédric Arhancet, Christoph Kriegler

We study the algebra $M^{\infty, dec} (G)$ of decomposable Fourier multipliers on the group von Neumann algebra $VN (G)$ of a locally compact group $G$ , a…

math.FA2022

Sobolev algebras on Lie groups and noncommutative geometry

Cédric Arhancet

We show that there exists a quantum compact metric space which underlies the setting of each Sobolev algebra associated to a subelliptic Laplacian $Δ = - (X_{1}^{2} + \dots + X_{m}^{2})$ on a co…

math.OA2022

Markov dilations of semigroups of Fourier multipliers

Cédric Arhancet

We describe a Markov dilation for any weak* continuous semigroup $(T_{t})_{t \geq 0}$ of selfadjoint unital completely positive Fourier multipliers acting on the group von Neumann al…

math.FA2021

A note on the Blum-Hanson property of some contractions on $L^{p}$ -spaces

Cédric Arhancet

If $Ω$ is a measure space, we show that absolute contractions which are selfadjoint on $L^{2} (Ω)$ induce contractions on $L^{p} (Ω)$ which satisfy the Blum-Hanson prop…

math.OA2020

Quantum information theory and Fourier multipliers on quantum groups

Cédric Arhancet

In this paper, we compute the exact values of the minimum output entropy and the completely bounded minimal entropy of very large classes of quantum channels acting on matrix algeb…

Radial Schur multipliers on trees and quantitative Fourier--Schur separation

A modular theory of contractive projections on Banach spaces with applications to noncommutative Lp-spaces

Multiplicativity of the weak Haagerup constant

Optimal square size for separating the operator and completely bounded norms of Schur multipliers on S4

Completely isometric subspaces of noncommutative Lp-spaces and contractive projections

Spectral nonassociative Lp-spaces for JBW∗-algebras

A reverse Riesz estimate combined with a spectral gap implies a Poincaré inequality

Spectral versus interpolation norms in tracial nonassociative Lp-spaces

On the convex structure of the space of quantum channels which act as Fourier multipliers

Dolbeault-Dirac operators on compact Kähler manifolds in Banach noncommutative geometry

The Lp-index of the Hodge-Dirac operator on compact Riemannian manifolds

Classical harmonic analysis viewed through the prism of noncommutative geometry

Functional calculus and semilinear evolution equations for the Taibleson operator on non-Archimedean local fields

Entanglement-assisted classical capacities of some channels acting as radial multipliers on fermion algebras

Curvature, Dolbeault-Dirac operators, and an Lp-index theorem on compact Kähler manifolds

The harmonic oscillator on the Moyal-Groenewold plane: an approach via Lie groups and twisted Weyl tuples

Nonassociative Lp-spaces and embeddings in noncommutative Lp-spaces

Separating Fourier and Schur multipliers

Spectral triples, Coulhon-Varopoulos dimension and heat kernel estimates

Decomposable Fourier Multipliers and an Operator-Algebraic Characterization of Amenability

Sobolev algebras on Lie groups and noncommutative geometry

Markov dilations of semigroups of Fourier multipliers

A note on the Blum-Hanson property of some contractions on Lp-spaces

Quantum information theory and Fourier multipliers on quantum groups

A modular theory of contractive projections on Banach spaces with applications to noncommutative $L^{p}$ -spaces

Optimal square size for separating the operator and completely bounded norms of Schur multipliers on $S^{4}$

Completely isometric subspaces of noncommutative $L^{p}$ -spaces and contractive projections

Spectral nonassociative $L^{p}$ -spaces for $JBW^{*}$ -algebras

Spectral versus interpolation norms in tracial nonassociative $L^{p}$ -spaces

The $L^{p}$ -index of the Hodge-Dirac operator on compact Riemannian manifolds

Curvature, Dolbeault-Dirac operators, and an $L^{p}$ -index theorem on compact Kähler manifolds

Nonassociative $L^{p}$ -spaces and embeddings in noncommutative $L^{p}$ -spaces

A note on the Blum-Hanson property of some contractions on $L^{p}$ -spaces