MC

M.P.T. Caspers

22 records found

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 order spectral shift functions. Our proof is ...
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 C[Γ] with Γ a discrete group. The starting point of this paper is that if a dense set of the so-called ...
Let W be a finitely generated right-angled Coxeter group with group von Neumann algebra L(W). We prove the following dichotomy: either L(W) is strongly solid or W contains Z×F2 as a subgroup. This proves in particular strong solidity of L(W) for all non-hyperbolic Coxeter groups ...
For a real Hilbert space HR and −1 < q < 1 Bozejko and Speicher introduced the C-algebra Aq(HR) and von Neumann algebra Mq(HR) of qGaussian variables. We prove that if dim(HR) = ∞ and −1 < q &l ...
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 the choice of the conditional expectation. ...
Let G be a semi-simple Lie group in the Harish-Chandra class with maximal compact subgroup K. Let ΩK be minus the radial Casimir operator. Let 1 4 dim(G/K) < SG < 1 2 dim(G/K), s ∈ (0, SG] and p ∈ (1,∞) be such that(1 p - 1 2 )< s 2SG . Then, there exists a constant CG,s ...
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. The obtained results extend various theor ...
Let Γ<G be a discrete subgroup of a locally compact unimodular group G. Let m∈C b(G) be a p-multiplier on G with 1≤p<∞ and let T m:L p(G^)→L p(G^) be the corresponding Fourie ...
Let πα be a holomorphic discrete series representation of a connected semi-simple Lie group G with finite center, acting on a weighted Bergman space Aα2(Ω) on a bounded symmetric domain Ω , of formal dimension dπα>0. It is shown that if the Bergman kernel kz(α) is a ...
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 noncommutative L p-spaces of the group von Neumann algeb ...
We consider semigroup BMO spaces associated with an arbitrary σ-finite von Neumann algebra (M, ϕ). We prove that BMO always admits a predual, extending results from the finite case. Consequently, we can prove—in the current setting of BMO—that they are Banach spaces and they inte ...
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 of central multipliers on a compact quant ...

Graph product Khintchine inequalities and Hecke C*-algebras

Haagerup inequalities, (non)simplicity, nuclearity and exactness

Graph products of groups were introduced by Green in her thesis [32]. They have an operator algebraic counterpart introduced and explored in [14]. In this paper we prove Khintchine type inequalities for general C⁎-algebraic graph products which generalize results by Ricard and Xu ...
Consider the generalized absolute value function defined by a(t) = | t| tn1, t∈ ℝ, n∈ ℕ≥ 1. Further, consider the n-th order divided difference function a[n]: ℝn+1 → ℂ and let 1 < p1, …, pn
We construct Markov semi-groups T and associated BMO-spaces on a finite von Neumann algebra (M,τ) and obtain results for perturbations of commutators and non-commutative Lipschitz estimates. In particular, we prove that for any A∈M self-adjoint and f:R→R Lipschitz there is a Mark ...
Consider the free orthogonal quantum groups ON+(F) and free unitary quantum groups UN+(F) with N≥ 3. In the case F= id N it was proved both by Isono and Fima-Vergnioux that the associated finite von Neumann algebra L∞(ON+) is strongly solid. Moreover, Isono obtains str ...
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-Sp estimates we analyze when these cocycles take values i ...
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 particular the following inclusions that follo ...
We discuss just infiniteness of C*-algebras associated to discrete quantum groups and relate it to the C*-uniqueness of the quantum groups in question, that is, to the uniqueness of a C*-completion of the underlying Hopf C*-algebra. It ...
We study certain q-deformed analogues of the maximal abelian subalgebras of the group von Neumann algebras of free groups. The radial subalgebra is defined for Hecke deformed von Neumann algebras of the Coxeter group (Z=2Z)k and shown to be a maximal abelian subalgebra ...