C. le Merdy

activity

20102026

most citedMaximal theorems and square functions for analytic operators on Lp-spaces

36 citations · 47 across the 21 of their papers we have counts for

collaborators

Showing math.FAShow all

15 papers · 1 filter

math.FA2024

Commuting families of polygonal type operators on Hilbert space

Christian Le Merdy, M. N. Reshmi

Let $T : H \to H$ be a bounded operator on Hilbert space. We say that $T$ has a polygonal type if there exists an open convex polygon $Δ \subset D$ , with $\overlineΔ\ca…

math.FA2024

A new approach to $γ$ -bounded representations

Christian Le Merdy

Let $X$ be a Banach space, let $(Ω, μ)$ be a $σ$ -finite measure space and let $A, B : Ω \to B (X)$ be strongly measurable $γ$ -bounded functions. We show that for all $x \in X$ and al…

math.FA2023

Hankel operators on $L^{p} (R_{+})$ and their $p$ -completely bounded multipliers

Loris Arnold, Christian Le Merdy, Safoura Zadeh

We show that for any $1 < p < \infty$ , the space $H an k_{p} (R_{+}) \subseteq B (L^{p} (R_{+}))$ of all Hankel operators on $L^{p} (R_{+})$ is equal to the $w^{*}$ -closure of th…

math.FA2022★ 2 cited

$S^{1}$ -bounded Fourier multipliers on $H^{1} (R)$ and functional calculus for semigroups

Loris Arnold, Christian Le Merdy, Safoura Zadeh

Let $T : H^{1} (R) \to H^{1} (R)$ be a bounded Fourier multiplier on the analytic Hardy space $H^{1} (R) \subset L^{1} (R)$ and let $m\in L^\infty({\m…

math.FA2022

Polygonal functional calculus for operators with finite peripheral spectrum

Oualid Bouabdillah, Christian Le Merdy

Let $T : X \to X$ be a bounded operator on Banach space, whose spectrum $σ (T)$ is included in the closed unit disc $D$ . Assume that the peripheral spectrum $σ…

math.FA2020

Functional calculus for a bounded $C_{0}$ -semigroup on Hilbert space

Loris Arnold, Christian Le Merdy

We introduce a new Banach algebra $A (C_{+})$ of bounded analytic functions on $C_{+} = {z \in C : Re (z) > 0}$ which is an analytic versio…

math.FA2017

Higher order $\Sc^2$-differentiability and application to Koplienko trace formula

Clément Coine, Christian Le Merdy, Anna Skripka +1

Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f \in C^{n} (R)$ . We establish that $φ (t) = f (A + t K) - f (A)$ is $n$ …

math.FA2017

When do triple operator integrals take value in the trace class?

Clément Coine, Christian Le Merdy, Fedor Sukochev

Consider three normal operators $A, B, C$ on separable Hilbert space $\H$ as well as scalar-valued spectral measures $λ_{A}$ on $σ (A)$ , $λ_{B}$ on $σ (B)$ and $λ_{C}$ on $σ (C)$ . For any $ϕ\…

math.FA2015

Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case

Clément Coine, Christian Le Merdy, Denis Potapov +2

We prove the existence of a complex valued $C^{2}$ -function on the unit circle, a unitary operator U and a self-adjoint operator Z in the Hilbert-Schmidt class $S^{2}$ , such that the p…

math.FA2015★ 2 cited

Isometric dilations and $H^{\infty}$ calculus for bounded analytic semigroups and Ritt operators

Cédric Arhancet, Stephan Fackler, Christian Le Merdy

We show that any bounded analytic semigroup on $L^{p}$ (with $1 < p < \infty$ ) whose negative generator admits a bounded $H^{\infty}$ functional calculus with respect to some angle $< π/…

math.FA2012

H^\infty functional calculus and square function estimates for Ritt operators

Christian Le Merdy

A Ritt operator T : X --> X on Banach space is a power bounded operator such that the sequence of all n(T^{n} -T^{n-1}) is bounded. When X=Lp for some 1<p<\infty, we study the vali…

math.FA2011★ 1 cited

A sharp equivalence between $H^{\infty}$ functional calculus and square function estimates

Christian Le Merdy

Let T_t = e^{-tA} be a bounded analytic semigroup on Lp, with 1<p<\infty. It is known that if A and its adjoint A^* both satisfy square function estimates \bignorm{\bigl(\int_{0}^{…

math.FA2011

Dilation of Ritt operators on L^{p}-spaces

Cedric Arhancet, Christian Le Merdy

For any Ritt operator T:L^{p}(Ω) --> L^{p}(Ω), for any positive real number α, and for any x in L^{p}, we consider the square functions |x |_{T,α} = \Bigl| \Bigl(\sum_{k=1}^{\infty…

math.FA2010★ 36 cited

Maximal theorems and square functions for analytic operators on Lp-spaces

Christian Le Merdy, Quanhua Xu

Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for…

math.FA2010

Gamma-bounded representations of amenable groups

Christian Le Merdy

Let G be an amenable group, let X be a Banach space and let π: G --> B(X) be a bounded representation. We show that if the set {π(t) : t \in G} is gamma-bounded then πextends to a…

Commuting families of polygonal type operators on Hilbert space

A new approach to γ-bounded representations

Hankel operators on Lp(R+​) and their p-completely bounded multipliers

S1-bounded Fourier multipliers on H1(R) and functional calculus for semigroups

Polygonal functional calculus for operators with finite peripheral spectrum

Functional calculus for a bounded C0​-semigroup on Hilbert space

Higher order $\Sc^2$-differentiability and application to Koplienko trace formula

When do triple operator integrals take value in the trace class?

Peller's problem concerning Koplienko-Neidhardt trace formulae: the unitary case

Isometric dilations and H∞ calculus for bounded analytic semigroups and Ritt operators

H^\infty functional calculus and square function estimates for Ritt operators

A sharp equivalence between H∞ functional calculus and square function estimates

Dilation of Ritt operators on L^{p}-spaces

Maximal theorems and square functions for analytic operators on Lp-spaces

Gamma-bounded representations of amenable groups

A new approach to $γ$ -bounded representations

Hankel operators on $L^{p} (R_{+})$ and their $p$ -completely bounded multipliers

$S^{1}$ -bounded Fourier multipliers on $H^{1} (R)$ and functional calculus for semigroups

Functional calculus for a bounded $C_{0}$ -semigroup on Hilbert space

Isometric dilations and $H^{\infty}$ calculus for bounded analytic semigroups and Ritt operators

A sharp equivalence between $H^{\infty}$ functional calculus and square function estimates