Cédric Arhancet

activity

20242026

collaborators

13 papers

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 PoincarÃ© inequality

CÃ©dric 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 $X$ in another Banach space $Y$ , we…

math.FA2026

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

CÃ©dric Arhancet, 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.FA2026

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

CÃ©dric Arhancet, 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.FA2026

Dolbeault-Dirac operators on compact KÃ¤hler manifolds in Banach noncommutative geometry

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

math.OA2026

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

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

Spectral nonassociative Lp-spaces for JBW∗-algebras

A reverse Riesz estimate combined with a spectral gap implies a PoincarÃ© inequality

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

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

Dolbeault-Dirac operators on compact KÃ¤hler manifolds in Banach noncommutative geometry

Spectral versus interpolation norms in tracial nonassociative Lp-spaces

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

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

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

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