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Comparing quantum dynamical entropies

P. Tuyls (1998)

Banach Center Publications

Last years, the search for a good theory of quantum dynamical entropy has been very much intensified. This is not only due to its usefulness in quantum probability but mainly because it is a very promising tool for the theory of quantum chaos. Nowadays, there are several constructions which try to fulfill this need, some of which are more mathematically inspired such as CNT (Connes, Narnhofer, Thirring), and the one proposed by Voiculescu, others are more inspired by physics such as ALF (Alicki,...

Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, Parasar Mohanty (2015)

Studia Mathematica

In this paper, we introduce and study the notion of completely bounded Λ p sets ( Λ p c b for short) for compact, non-abelian groups G. We characterize Λ p c b sets in terms of completely bounded L p ( G ) multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are Λ p sets for all p < ∞, but are not Λ p c b for any p ≥ 4. This is done by showing that the space of completely bounded L p ( G ) multipliers...

Computation of some examples of Brown's spectral measure in free probability

Philippe Biane, Franz Lehner (2001)

Colloquium Mathematicae

We use free probability techniques to compute spectra and Brown measures of some non-hermitian operators in finite von Neumann algebras. Examples include u ₙ + u ∞ where uₙ and u ∞ are the generators of ℤₙ and ℤ respectively, in the free product ℤₙ*ℤ, or elliptic elements of the form S α + i S β where S α and S β are free semicircular elements of variance α and β.

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