Éric Ricard
YOU?
Author Swipe
View article: Quasi-invariant states with uniformly bounded cocycles
Quasi-invariant states with uniformly bounded cocycles Open
We investigate the notion of quasi-invariant states introduced in [2, 3] from an analytic viewpoint.We give the structures of quasi-invariant states with uniformly bounded cocycles. As a consequence, we can apply a Theorem of Kovacs and Sz…
View article: Riesz-Schur transforms
Riesz-Schur transforms Open
We investigate nontrigonometric forms of Riesz transforms in the context of Schur multipliers. This refines Grothendieck-Haagerup's endpoint criterion with a new condition for the Schatten p-boundedness of Schur multipliers and strengthens…
View article: Failure of almost uniformly convergence for noncommutative martingales
Failure of almost uniformly convergence for noncommutative martingales Open
In this paper, we provide a counterexample to show that in sharp contrast to the classical case, the almost uniform convergence may not happen for truly noncommutative $L_p$-martingales when $1\leq p<2$. The same happens to ergodic average…
View article: Calderón-Zygmund theory with noncommuting kernels via $H_1^c$
Calderón-Zygmund theory with noncommuting kernels via $H_1^c$ Open
We study an alternative definition of the $H_1$-space associated to a semicommutative von Neumann algebra $L_\infty(\mathbb{R}) \overline{\otimes} \mathcal{M}$, first studied by Mei. We identify a "new" description for atoms in $H_1$. We t…
View article: Revisiting the Marcinkiewicz theorem for non commutative maximal functions
Revisiting the Marcinkiewicz theorem for non commutative maximal functions Open
We give an alternative proof of a Marcinkiewicz interpolation theorem for non commutative maximal functions and positive maps, slightly refining earlier versions of the statement. The main novelty is that it provides a substitute for the m…
View article: Fourier multipliers in SLn(R)
Fourier multipliers in SLn(R) Open
We establish precise regularity conditions for Lp-boundedness of Fourier multipliers\nin the group algebra of SLn.R/. Our main result is inspired by the Hörmander¿\nMikhlin criterion from classical harmonic analysis, although it is substan…
View article: On the factoriality of q-deformed Araki-Woods von Neumann algebras
On the factoriality of q-deformed Araki-Woods von Neumann algebras Open
The $q$-deformed Araki-Woods von Neumann algebras $Γ_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ are factors for all $q\in (-1,1)$ whenever $dim(\mathcal{H}_\mathbb{R})\geq 3$. When $dim(\mathcal{H}_\mathbb{R})=2$ they are factors as w…
View article: A Hörmander-Mikhlin multiplier theory for free groups and amalgamated free products of von Neumann algebras
A Hörmander-Mikhlin multiplier theory for free groups and amalgamated free products of von Neumann algebras Open
We establish a platform to transfer $L_p$-completely bounded maps on tensor products of von Neumann algebras to $L_p$-completely bounded maps on the corresponding amalgamated free products. As a consequence, we obtain a Hörmander-Mikhlin m…
View article: Fourier multipliers in $\mathrm{SL}_n(\mathbf{R})$
Fourier multipliers in $\mathrm{SL}_n(\mathbf{R})$ Open
We establish precise regularity conditions for $L_p$-boundedness of Fourier multipliers in the group algebra of $SL_n(\mathbf{R})$. Our main result is inspired by Hörmander-Mikhlin criterion from classical harmonic analysis, although it is…
View article: Fractional powers on noncommutative $L_p$ for $p<1$
Fractional powers on noncommutative $L_p$ for $p<1$ Open
We prove that the homogeneous functional calculus associated to $x\mapsto |x|^\theta$ or $x\mapsto {\rm sgn}\, (x) |x|^{\theta}$ for $0<\theta<1$ is $\theta$-H\"older on selfadjoint elements of noncommutative $L_p$-spaces for $0<p\leq\inft…
View article: Fractional powers on noncommutative $L_p$ for $p<1$
Fractional powers on noncommutative $L_p$ for $p<1$ Open
We prove that the homogeneous functional calculus associated to $x\mapsto |x|^θ$ or $x\mapsto {\rm sgn}\, (x) |x|^θ$ for $0
View article: Free Hilbert transforms
Free Hilbert transforms Open
We study analogues of classical Hilbert transforms as fourier multipliers on\nfree groups. We prove their complete boundedness on non commutative $L^p$\nspaces associated with the free group von Neumann algebras for all\n$1<p<\\infty$. Thi…
View article: On spectral gaps of Markov maps
On spectral gaps of Markov maps Open
It is shown that if a Markov map $T$ on a noncommutative probability space $\mathcal{M}$ has a spectral gap on $L_2(\mathcal{M})$, then it also has one on $L_p(\mathcal{M})$ for $1
View article: An inequality in noncommutative $L_p$-spaces
An inequality in noncommutative $L_p$-spaces Open
We prove that for any (trace-preserving) conditional expectation $\mathcal E$ on a noncommutative $L_p$ with $p>2$, $Id-\mathcal E$ is a contraction on the positive cone $L_p^+$.
View article: $L_p$-Multipliers on Quantum Tori
$L_p$-Multipliers on Quantum Tori Open
It was shown by Chen, Xu and Yin that completely bounded Fourier multipliers on noncommutative $L_p$-spaces of quantum tori $\mathbb T^d_θ$ do not depend on the parameter $θ$. We establish that the situation is somehow different for bounde…
View article: NONCOMMUTATIVE DE LEEUW THEOREMS
NONCOMMUTATIVE DE LEEUW THEOREMS Open
Let $\text{H}$ be a subgroup of some locally compact group $\text{G}$ . Assume that $\text{H}$ is approximable by discrete subgroups and that $\text{G}$ admits neighborhood bases which are almost invariant under conjugation by finite subse…