We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main
result is a Hörmander–Mihlin multiplier theorem for finite-dimensional cocycles with optimal …

We give a brief survey of many of the high-lights of our present understanding of the young
subject of quantum metric spaces, and of quantum Gromov-Hausdorff distance between …

We introduce the quantum Gromov-Hausdorff propinquity, a new distance between quantum
compact metric spaces, which extends the Gromov-Hausdorff distance to noncommutative …

Abstract For $2\le p<\infty $ we show the lower estimates $$\| A^{\frac 12} x\| _p\le c
(p)\max\{\|\Gamma (x, x)^{\frac {1}{2}}\| _p,\|\Gamma (x^*, x^*)^{\frac {1}{2}}\| _p\} $$ for the …

An AF C*-algebra has a natural filtration as an increasing sequence of finite dimensional C*-
algebras. We show that it is possible to construct a Dirac operator which relates to this …

We construct quantum metric structures on unital AF algebras with a faithful tracial state, and
prove that for such metrics, AF algebras are limits of their defining inductive sequences of …

In the context of metric geometry, we introduce a new necessary and sufficient condition for
the convergence of an inductive sequence of quantum compact metric spaces for the …

Motivated by the quest for an analogue of the Gromov–Hausdorff distance in
noncommutative geometry which is well-behaved with respect to C⁎-algebraic structures …

We prove a deviation inequality for noncommutative martingales by extending Oliveira's
argument for random matrices. By integration we obtain a Burkholder type inequality with …

Let (A, H, D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A
acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A …