On the factoriality of q-deformed Araki-Woods von Neumann algebras

Autor: Panchugopal Bikram, Kunal Mukherjee, Éric Ricard, Simeng Wang

The $q$-deformed Araki-Woods von Neumann algebras $\Gamma_q(\mathcal{H}_\mathbb{R}, U_t)^{\prime \prime}$ 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 well fo

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3f6545e611c98ad1b8153f8ee6d3fec4

NONCOMMUTATIVE DE LEEUW THEOREMS

Autor: MARTIJN CASPERS, JAVIER PARCET, MATHILDE PERRIN, ÉRIC RICARD

Publikováno v: Forum of Mathematics, Sigma, Vol 3 (2015)

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 subsets of $\text

Externí odkaz: https://doaj.org/article/831e4c088a954eafb145e66ba1ee61c6

An $L_p$-inequality for anticommutators

Autor: Éric Ricard

Publikováno v: Integral Equations and Operator Theory
Integral Equations and Operator Theory, Springer Verlag, 2021, 93 (1), ⟨10.1007/s00020-020-02622-4⟩

We prove a basic inequality involving anticommutators in noncommutative $$L_p$$ -spaces. We use it to complete our study of the noncommutative Mazur maps from $$L_p$$ to $$L_q$$ showing that they are Lipschitz on balls when $$0

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7a253ba8335bd0c3c6d54eeebbd0d35
http://arxiv.org/abs/2012.02566

An extension of inequalities by Ando

Autor: Éric Ricard

Publikováno v: Linear Algebra and its Applications
Linear Algebra and its Applications, Elsevier, 2019, ⟨10.1016/j.laa.2019.06.029⟩

We give variations on Ando's result comparing f ( B ) − f ( A ) and f ( | B − A | ) with respect to unitarily invariant norms on matrices.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb14655cff46f44b97ea1985790852b8

On spectral gaps of Markov maps

Autor: Éric Ricard, Javier Parcet, José M. Conde-Alonso

Publikováno v: Digital.CSIC. Repositorio Institucional del CSIC
instname
Israël Journal of Mathematics
Israël Journal of Mathematics, Hebrew University Magnes Press, 2018, 226 (1), pp.189-203. ⟨10.1007/s11856-018-1693-1⟩

It is shown that if a Markov map T on a noncommutative probability space M has a spectral gap on L(M), then it also has one on L(M) for 1 < p < ∞. For fixed p, the converse also holds if T is factorizable. Some results are also new for classical pr

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e6ad467fc94c1a0b63dd063c5b81760
http://hdl.handle.net/10261/253303