10 citations · 67 across the 20 of their papers we have counts for
20 papers
Empirical bounds for commuting dilations of free unitaries and the universal commuting dilation constant
Malte Gerhold, Marcel Scherer, Orr Shalit
For a tuple of Hilbert space operators, the 'commuting dilation constant' is the smallest number such that the operators of are a simultaneous compression of commuting…
Dilation distance and the stability of ergodic commutation relations
Malte Gerhold, Orr Shalit
We revisit and generalize the notion of dilation distance between unitary tuples and study its relation to the natural Haagerup-Rørdam distance ${\rm d_{HR}}(u,v…
Linear Deformations of Heisenberg Modules and Gabor Frames
Malte Gerhold, Arvin Lamando, Franz Luef
Heisenberg modules over noncommutative tori may also be viewed as Gabor frames. Building on this fact, we relate to deformations of noncommutative tori a bundle of Banach spaces in…
Free resolutions for free unitary quantum groups and universal cosovereign Hopf algebras
Isabelle Baraquin, Uwe Franz, Malte Gerhold +2
We find a finite free resolution of the counit of the free unitary quantum groups of van Daele and Wang and, more generally, Bichon's universal cosovereign Hopf algebras with a gen…
Towards a classification of multi-faced independences: a combinatorial approach
Malte Gerhold, Philipp Varšo
We determine a set of necessary conditions on a partition-indexed family of complex numbers to be the "highest coefficients" of a positive and symmetric multi-faced universal produ…
Bounded perturbations of the Heisenberg commutation relation via dilation theory
Malte Gerhold, Orr Shalit
We extend the notion of dilation distance to strongly continuous one-parameter unitary groups. If the dilation distance between two such groups is finite, then these groups can be…
Shuffle Algebras and Non-Commutative Probability for Pairs of Faces
Joscha Diehl, Malte Gerhold, Nicolas Gilliers
One can build an operatorial model for freeness by considering either the right-handed or the left-handed representation of algebras of operators acting on the free product of the…
Towards a Classification of Multi-Faced Independence: A Representation-Theoretic Approach
Malte Gerhold, Takahiro Hasebe, Michael Ulrich
We attack the classification problem of multi-faced independences, the first non-trivial example being Voiculescu's bi-freeness. While the present paper does not achieve a complete…
Schoenberg correspondence for multifaced independence
Malte Gerhold
We extend the Schoenberg correspondence for universal independences by Schürmann \& Voß to the multivariate setting of Manzel \& Schürmann, covering, e.g., Voiculescu's bifreeness…
Dilations of unitary tuples
Malte Gerhold, Satish K. Pandey, Orr Shalit +1
We study the space of all -tuples of unitaries using dilation theory and matrix ranges. Given two -tuples and generating C*-algebras $\mathcal A…
On the matrix range of random matrices
Malte Gerhold, Orr Shalit
This note treats a simple minded question: what does a typical random matrix range look like? We study the relationship between various modes of convergence for tuples of operators…
Dilations of -commuting unitaries
Malte Gerhold, Orr Shalit
Let (where ), and let be -commuting unitaries, i.e., and are unitaries such that . In this paper we find th…
Interacting Fock Spaces and Subproduct Systems
Malte Gerhold, Michael Skeide
We prove many new results about interacting Fock spaces. We pose many open problems; for most of them we prove that their solutions have no choice but being nontrivial. We ask the…
Bimonotone Brownian Motion
Malte Gerhold
We define bi-monotone independence, prove a bi-monotone central limit theorem and use it to study the distribution of bi-monotone Brownian motion, which is defined as the two-dimen…
Homological properties of quantum permutation algebras
Julien Bichon, Uwe Franz, Malte Gerhold
We show that , the coordinate algebra of Wang's quantum permutation group, is Calabi-Yau of dimension when , and compute its Hochschild cohomology with trivial…
Categorial Independence and Lévy Processes
Malte Gerhold, Stephanie Lachs, Michael Schürmann
We generalize Franz' independence in tensor categories with inclusions from two morphisms (which represent generalized random variables) to arbitrary ordered families of morphisms.…
On the Lévy-Khinchin decomposition of generating functionals
Uwe Franz, Malte Gerhold, Andreas Thom
We study several sufficient conditions for the existence of a Lévy-Khinchin decomposition of generating functionals. We show that none of these conditions are equivalent and we sho…
Subproduct systems and Cartesian systems; new results on factorial languages and their relations with other areas
Malte Gerhold, Michael Skeide
We point out that a sequence of natural numbers is the dimension sequence of a subproduct system if and only if it is the cardinality sequence of a word system (or factorial langua…
Additive Deformations of Braided Hopf Algebras
Malte Gerhold, Stefan Kietzmann, Stephanie Lachs
Additive deformations of bialgebras in the sense of J. Wirth, i.e. deformations of the multiplication map fulfilling a certain compatibility condition w.r.t. the coalgebra structur…
Additive Deformations of Hopf Algebras
Malte Gerhold
Additive deformations of bialgebras in the sense of Wirth are deformations of the multiplication map of the bialgebra fulfilling a compatibility condition with the coalgebra struct…