Martijn Caspers
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View article: Higher order perturbation estimates in quasi-Banach Schatten spaces through wavelets
Higher order perturbation estimates in quasi-Banach Schatten spaces through wavelets Open
Let $n \in \mathbb{N}_{\geq 1}$. Let $1 \leq p_1, \ldots, p_n < \infty$ and set the Hölder combination $p := (p_1; \ldots ; p_n) := \left( \sum_{j=1}^n p_j^{-1} \right)^{-1}$. Assume further that $0 < p \leq 1$ and that for the Hölder comb…
View article: Internal graphs of graph products of hyperfinite II$_1$-factors
Internal graphs of graph products of hyperfinite II$_1$-factors Open
In this paper, we show that for a graph $Γ$ from a class named H-rigid graphs, its subgraph ${\rm Int}(Γ)$, named the internal graph of $Γ$, is an isomorphism invariant of the graph product of hyperfinite II$_1$-factors $R_Γ$. In particula…
View article: Rigid Graph Products
Rigid Graph Products Open
We prove rigidity properties for von Neumann algebraic graph products. We introduce the notion of rigid graphs and define a class of II$_1$-factors named $\mathcal{C}_{\rm Rigid}$. For von Neumann algebras in this class we show a unique ri…
View article: On the best constants of Schur multipliers of second order divided difference functions
On the best constants of Schur multipliers of second order divided difference functions Open
We give a new proof of the boundedness of bilinear Schur multipliers of second order divided difference functions, as obtained earlier by Potapov, Skripka and Sukochev in their proof of Koplienko's conjecture on the existence of higher ord…
View article: Bimodule coefficients, Riesz transforms on Coxeter groups and strong solidity
Bimodule coefficients, Riesz transforms on Coxeter groups and strong solidity Open
In deformation-rigidity theory, it is often important to know whether certain bimodules are weakly contained in the coarse bimodule. Consider a bimodule H over the group algebra \mathbb{C}[\Gamma] with \Gamma a discrete group. The starting…
View article: Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra
Classification of right-angled Coxeter groups with a strongly solid von Neumann algebra Open
Let $W$ be a finitely generated right-angled Coxeter group with group von Neumann algebra $\mathcal{L}(W)$. We prove the following dichotomy: either $\mathcal{L}(W)$ is strongly solid or $W$ contains $\mathbb{Z} \times \mathbb{F}_2$ as a s…
View article: A Sobolev estimate for radial $L^p$-multipliers on a class of semi-simple Lie groups
A Sobolev estimate for radial $L^p$-multipliers on a class of semi-simple Lie groups Open
Let $G$ be a semi-simple Lie group in the Harish-Chandra class with maximal compact subgroup $K$. Let $Ω_K$ be minus the radial Casimir operator. Let $\frac{1}{4} \dim(G/K) < S_G < \frac{1}{2} \dim(G/K) , s \in (0, S_G]$ and $p \in (1,\inf…
View article: Erratum to “BMO spaces of $\sigma $-finite von Neumann algebras and Fourier–Schur multipliers on SU$_q(2)$” (Studia Mathematica 262 (2022), 45–91)
Erratum to “BMO spaces of $\sigma $-finite von Neumann algebras and Fourier–Schur multipliers on SU$_q(2)$” (Studia Mathematica 262 (2022), 45–91) Open
This erratum addresses an error in Appendix A, where the construction of a canonical compatible couple structure from a so-called intersection mapping was attempted. It turns out that this requires an extra condition, which is not clear fo…
Multilinear transference of Fourier and Schur multipliers acting on noncommutative -spaces Open
Let G be a locally compact unimodular group, and let $\phi $ be some function of n variables on G . To such a $\phi $ , one can associate a multilinear Fourier multiplier, which acts on some n -fold product of the noncommutative $L_p$ -spa…
View article: On the isomorphism class of $q$-Gaussian W$^\ast$-algebras for infinite variables
On the isomorphism class of $q$-Gaussian W$^\ast$-algebras for infinite variables Open
Let $M_q(H_{\mathbb{R}})$ be the $q$-Gaussian von Neumann algebra associated with a separable infinite dimensional real Hilbert space $H_{\mathbb{R}}$ where $-1 < q < 1$. We show that $M_q(H_{\mathbb{R}}) \not \simeq M_0(H_{\mathbb{R}})$ f…
View article: Overcompleteness of coherent frames for unimodular amenable groups
Overcompleteness of coherent frames for unimodular amenable groups Open
This paper concerns the overcompleteness of coherent frames for unimodular amenable groups. It is shown that for coherent frames associated with a localized vector a set of positive Beurling density can be removed yet still leave a frame. …
View article: Multilinear transference of Fourier and Schur multipliers acting on non-commutative $L_p$-spaces
Multilinear transference of Fourier and Schur multipliers acting on non-commutative $L_p$-spaces Open
Let $G$ be a locally compact unimodular group, and let $ϕ$ be some function of $n$ variables on $G$. To such a $ϕ$, one can associate a multilinear Fourier multiplier, which acts on some $n$-fold product of the non-commutative $L_p$-spaces…
View article: On the isomorphism class of $q$-Gaussian C$^\ast$-algebras for infinite variables
On the isomorphism class of $q$-Gaussian C$^\ast$-algebras for infinite variables Open
For a real Hilbert space $H_{\mathbb{R}}$ and $-1 < q < 1$ Bozejko and Speicher introduced the C$^\ast$-algebra $A_q(H_{\mathbb{R}})$ and von Neumann algebra $M_q(H_{\mathbb{R}})$ of $q$-Gaussian variables. We prove that if $\dim(H_{\mathb…
View article: Local and multilinear noncommutative de Leeuw theorems
Local and multilinear noncommutative de Leeuw theorems Open
Let $Γ< G$ be a discrete subgroup of a locally compact unimodular group $G$. Let $m\in C_b(G)$ be a $p$-multiplier on $G$ with $1 \leq p < \infty$ and let $T_{m}: L_p(\widehat{G}) \rightarrow L_p(\widehat{G})$ be the corresponding Fourier …
View article: Relative Haagerup property for arbitrary von Neumann algebras
Relative Haagerup property for arbitrary von Neumann algebras Open
We introduce the relative Haagerup approximation property for a unital, expected inclusion of arbitrary von Neumann algebras and show that if the smaller algebra is finite then the notion only depends on the inclusion itself, and not on th…
View article: Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains
Density conditions with stabilizers for lattice orbits of Bergman kernels on bounded symmetric domains Open
Let $π_α$ be a holomorphic discrete series representation of a connected semi-simple Lie group $G$ with finite center, acting on a weighted Bergman space $A^2_α (Ω)$ on a bounded symmetric domain $Ω$, of formal dimension $d_{π_α} > 0$. It …
View article: Bimodule coefficients, Riesz transforms on Coxeter groups and strong solidity
Bimodule coefficients, Riesz transforms on Coxeter groups and strong solidity Open
In deformation-rigidity theory it is often important to know whether certain bimodules are weakly contained in the coarse bimodule. Consider a bimodule $H$ over the group algebra $\mathbb{C}[Γ]$, with $Γ$ a discrete group. The starting poi…
View article: RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY
RIESZ TRANSFORMS ON COMPACT QUANTUM GROUPS AND STRONG SOLIDITY Open
One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semigroups and noncommutative Riesz transforms. We introduce a property for quantum Markov semigroups …
View article: BMO spaces of $\sigma$-finite von Neumann algebras and Fourier-Schur multipliers on $SU_q(2)$
BMO spaces of $\sigma$-finite von Neumann algebras and Fourier-Schur multipliers on $SU_q(2)$ Open
We consider semi-group BMO spaces associated with an arbitrary $\sigma$-finite von Neumann algebra $(\mathcal{M}, \varphi)$. We prove that the associated row and column BMO spaces always admit a predual, extending results from the finite c…
View article: Riesz transforms on compact quantum groups and strong solidity
Riesz transforms on compact quantum groups and strong solidity Open
One of the main aims of this paper is to give a large class of strongly solid compact quantum groups. We do this by using quantum Markov semi-groups (QMS's) and non-commutative Riesz transforms. We introduce a property for QMS's of central…
View article: Weak $(1,1)$ estimates for multiple operator integrals and generalized\n absolute value functions
Weak $(1,1)$ estimates for multiple operator integrals and generalized\n absolute value functions Open
Consider the generalized absolute value function defined by \\[ a(t) = \\vert t\n\\vert t^{n-1}, \\qquad t \\in \\mathbb{R}, n \\in \\mathbb{N}_{\\geq 1}. \\] Further,\nconsider the $n$-th order divided difference function $a^{[n]}:\n\\mat…
View article: Graph product Khintchine inequalities and Hecke C*-algebras: Haagerup\n inequalities, (non)simplicity, nuclearity and exactness
Graph product Khintchine inequalities and Hecke C*-algebras: Haagerup\n inequalities, (non)simplicity, nuclearity and exactness Open
Graph products of groups were introduced by Green in her thesis. They have an\noperator algebraic counterpart introduced and explored by Fima and the\nfirst-named author. In this paper we prove Khintchine type inequalities for\ngeneral C$^…
View article: $L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebras
$L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebras Open
We study (quasi-)cohomological properties through an analysis of quantum Markov semi-groups. We construct higher order Hochschild cocycles using gradient forms associated with a quantum Markov semi-group. By using Schatten-$\mathcal{S}_p$ …
View article: On the complete bounds of $$L_p$$ L p -Schur multipliers
On the complete bounds of $$L_p$$ L p -Schur multipliers Open
We study the class Mp of Schur multipliers on the Schatten-von Neumann class Sp with 1 ≤ p≤ ∞ as well as the class of completely bounded Schur multipliers Mpcb. We first show that for 2 ≤ p< q≤ ∞ there exists m∈Mpcb with m∉ Mq, so in pa…
View article: On the complete bounds of $L_p$-Schur multipliers
On the complete bounds of $L_p$-Schur multipliers Open
We study the class $\mathcal{M}_p$ of Schur multipliers on the Schatten-von Neumann class $\mathcal{S}_p$ with $1 \leq p \leq \infty$ as well as the class of completely bounded Schur multipliers $\mathcal{M}_p^{cb}$. We first show that for…