Cédric Arhancet

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20182026

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10 papers · 1 filter

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 an Abel-ergodic sectorial operator $A$ on a Banach space $X$ and an unbounded operator $\partial$ defined on a subspace of $X$ in another Banach space $Y$ ,…

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 $L^{p}$ …

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

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

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

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

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