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Research interests
- Quantum groups
- Operator algebras
- Operator spaces and their approximation properties
- Non-commutative Lp-spaces
- Harmonic analysis on non-commutative spaces
Papers and preprints
Any comment, suggestion or question is more than welcome. "Final version" indicates that the ArXiv-version agrees with the version that was sent for the publication process.
Preprints
- "BMO spaces of sigma-finite von Neumann algebras and Fourier-Schur multipliers on quantum SU(2)".
with Gerrit Vos.
preprint.
- "Riesz transforms on compact quantum groups and strong solidity".
preprint.
- "Weight theory for ultraproducts".
preprint.
Papers (in press)
- "Gradient forms and strong solidity of free quantum groups".
Accepted for Mathematische Annalen.
preprint (final version).
- "Weak (1,1) estimates for multiple operator integrals and generalized absolute value functions".
with Fedor Sukochev and Dmitriy Zanin.
Accepted for Israel Journal of Mathematics.
preprint (final version).
- "L2-cohomology, derivations and quantum Markov semi-groups on q-Gaussian algebras".
with Yusuke Isono and Mateusz Wasilewski.
Accepted for IMRN.
preprint (final version).
- "Graph product Khintchine inequalities and Hecke C*-algebras: Haagerup inequalities, (non)simplicity, nuclearity and exactness".
with Mario Klisse and Nadia Larsen.
J. Funct. Anal. 280 (2021), no. 1, 108795.
preprint (final version).
- "Absence of Cartan subalgebras for right-angled Hecke von Neumann algebras".
Anal. PDE 13 (2020), no. 1, 1--28.
preprint (final version), erratum.
- "BMO-estimates for non-commtutative vector valued Lipschitz functions".
with Marius Junge, Fedor Sukochev, Dima Zanin.
J. Funct. Anal. 278 (2020), no. 3, 108317.
preprint (final version).
- "On MASAs in q-deformed von Neumann algebras".
with Adam Skalski and Mateusz Wasilewski.
Pacific J. Math. 302 (2019), no. 1, 1--21.
preprint (final version).
- "Weak type commutator and Lipschitz estimates: resolution of the Nazarov-Peller conjecture".
with Denis Potapov, Fedor Sukochev and Dmitriy Zanin.
Amer. J. Math. 141 (2019), no. 3, 593–610.
preprint (final version).
- "On the complete bounds of Lp-Schur multipliers".
with Guillermo Wildschut.
Arch. Math. (Basel) 113 (2019), no. 2, 189–200.
preprint (final version).
- "On C*-completions of discrete quantum group rings".
with Adam Skalski.
Bull. London Math. Soc. 51 (2019), no. 4, 691-704.
preprint (final version).
- "Harmonic analysis and BMO-spaces of free Araki-Woods factors".
Studia Math. 246 (2019), no. 1, 71–107.
preprint (final version).
- "Weak type operator Lipschitz and commutator estimates for commuting tuples".
with Fedor Sukochev and Dmitriy Zanin.
Ann. Inst. Fourier (Grenoble) 68 (2018), no. 4, 1643–1669.
preprint (final version).
- "Graph products of operator algebras".
with Pierre Fima.
J. Noncommut. Geom. 11 (2017), no. 1, 367-411.
preprint (final version).
- "Connes embeddability of graph products".
Infin. Dimens. Anal. Quantum Probab. Relat. Top. 19 (2016), no. 1, 1650004, 13 pp.
preprint (final version).
- "Operator biflatness of the L1-algebras of compact quantum groups".
with Hun Hee Lee and Eric Ricard.
J. Reine Angew. Math. 700 (2015), 235-244.
preprint (final version).
- "Schur and Fourier multipliers of an amenable group acting on non-commutative Lp-spaces".
with Mikael de la Salle.
Trans. Amer. Math. Soc. 367 (2015), no. 10, 6997-7013.
preprint (final version).
- "The Haagerup approximation property for von Neumann algebras via quantum Markov semigroups and Dirichlet forms".
with Adam Skalski.
Comm. Math. Phys. 336 (2015), no. 3, 1637-1664.
preprint (final version).
- "Noncommutative de Leeuw theorems".
with Javier Parcet, Mathilde Perrin, Eric Ricard.
Forum of Mathematics - Sigma 3 (2015), e21.
preprint (not final but journal is open access).
- "The Haagerup property for arbitrary von Neumann algebras".
with Adam Skalski.
Int. Math. Res. Not. IMRN 2015, no. 19, 9857-9887.
preprint (final version).
- "Weak type estimates for the absolute value mapping".
with Denis Potapov, Fedor Sukochev and Dima Zanin.
J. Operator Theory 73 (2015), no. 2, 361-384.
preprint (final version).
- "The best constants for operator Lipschitz functions on Schatten classes".
with Stephen Montgomery-Smith, Denis Potapov and Fedor Sukochev.
J. Funct. Anal. 267 (2014), no. 10, 3557-3579.
preprint (final version).
- "Weak amenability of locally compact quantum groups and approximation properties of extended quantum SU(1,1)".
Comm. Math. Phys. 331 (2014), no. 3, 1041-1069.
preprint (final version).
- "Generalisations of the Haagerup approximation property to
arbitrary von Neumann algebras".
with Rui Okayasu, Adam Skalski, Reiji Tomatsu.
C. R. Acad. Sci. Paris, Ser. I 352 (2014) 507-510
preprint (final version).
- "The Walsh basis in the Lp-spaces of hyperfinite III_\lambda factors, 0 < \lambda <=1".
with Denis Potapov and Fedor Sukochev.
J. Math. Anal. Appl. 408 (2013), 154-164
preprint (final version), journal.
- "The L^p-Fourier transform on locally compact quantum groups".
J. Operator Theory 69 (2013), 161-193
preprint (final version), journal
- "Spherical Fourier transforms on locally compact quantum Gelfand pairs".
SIGMA 7 (2011), 087, 39 pages.
paper (final version), journal.
- "Modular properties of matrix coefficients of corepresentations of a locally compact quantum group".
Together with Erik Koelink.
J. Lie Theory 21 (2011), no. 4, 905-928.
preprint (final version), journal.
- "Intuitionistic quantum logic of an n-level system".
Together with Chris Heunen, Klaas Landsman and Bas Spitters.
Foundations of Physics 39 (2009), No. 7, 731-759.
preprint (final version), journal.
Other
- "On the endpoints of De Leeuw restriction theorems". 2018
Chapter in Festschrift on the occassion of Ben de Pagter's 65th anniversary.
link.
- "Locally compact quantum groups". Lecture notes, Bedlewo 2015.
Banach Center Publications 111 (2017), 153-184.
link.
- "Noncommutative De Leeuw theorems". Noncommutative geometry. Oberwolfach Reports 2 (2015), 1631-1700.
link.
- "Hecke von Neumann algebras, operator spaces and absence of Cartan subalgebras". Noncommutative geometry and operator spaces in interaction. Oberwolfach Reports, 2016.
link.
- "Gradient forms and strong solidity of free quantum groups". Interactions between Operator Space Theory and Quantum Probability with Applications to
Quantum Information. Oberwolfach Reports, 2018.
link.
- "Quantum groups and special functions". Winter school in Bizerte, Tunisia, 2010.
Prepared together with Erik Koelink.
notes.
Thesis
- "Non-commutative integration on locally compact quantum groups" (PhD Thesis 2012).
Adviser: Erik Koelink
Download: Thesis.
- "Gelfand spectra of C*-algebras in topos theory" (MSc. Thesis 2008).
Under supervision of Klaas Landsman.
Awarded with the GQT MSc. thesis prize.
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