The von Neumann algebra generated by t-gaussians

We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ sufficiently close to 1, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness

On the algebraic structure of the unitary group

We consider the unitary group \U of complex, separable, infinite-dimensional Hilbert space as a discrete group. It is proved that, whenever \U acts by isometries on a metric space, every orbit is bounded. Equivalently, \U is not the union of a countable chain of proper subgroups, and whenever \E\subseteq \U generates \U, it does so by words of a fixed finite length

On contractive projections in Hardy spaces

We prove a conjecture of Wojtaszczyk that for $1\leq p<\infty$, $p\neq 2$, H_p(\mathbbT) does not admit any norm one projections with dimension of the range finite and bigger than 1. This implies in particular that for $1\leq p<\infty$, $p\ne 2$, $H_p$ does not admit a Schauder basis with constant one.Comment: 9 pages, to appear in Studia Mathematic

A global shear velocity model of the upper mantle from fundamental and higher Rayleigh mode measurements

International audienceWe present DR2012, a global SV-wave tomographic model of the upper mantle. We use an extension of the automated waveform inversion approach of Debayle (1999) which improves our mapping of the transition zone with extraction of fundamental and higher-mode information. The new approach is fully automated and has been successfully used to match approximately 375,000 Rayleigh waveforms. For each seismogram, we obtain a path average shear velocity and quality factor model, and a set of fundamental and higher-mode dispersion and attenuation curves. We incorporate the resulting set of path average shear velocity models into a tomographic inversion. In the uppermost 200 km of the mantle, SV wave heterogeneities correlate with surface tectonics. The high velocity signature of cratons is slightly shallower (approximate to 200 km) than in other seismic models. Thicker continental roots are not required by our data, but can be produced by imposing a priori a smoother model in the vertical direction. Regions deeper than 200 km show no velocity contrasts larger than +/- 1\% at large scale, except for high velocity slabs within the transition zone. Comparisons with other seismic models show that current surface wave datasets allow to build consistent models up to degrees 40 in the upper 200 km of the mantle. The agreement is poorer in the transition zone and confined to low harmonic degrees (<= 10)

Experimental evidence of random shock-wave intermittency

We report the experimental observation of intermittency in a regime dominated by random shock waves on the surface of a fluid. We achieved such a nondispersive surface-wave field using a magnetic fluid subjected to a high external magnetic field. We found that the small-scale intermittency of the wave-amplitude fluctuations is due to shock waves, leading to much more intense intermittency than previously reported in three-dimensional hydrodynamics turbulence or in wave turbulence. The statistical properties of intermittency are found to be in good agreement with the predictions of a Burgerslike intermittency model. Such experimental evidence of random shock-wave intermittency could lead to applications in various fields