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Ad un'algebra di von Neumann separabile , in forma standard su di uno spazio di Hilbert , si associa la algebra definita come la algebra costituita dai punti fissi dell'algebra di Cuntz generalizzata mediante l'azione canonica del gruppo degli unitari di . Si dà una caratterizzazione di nel caso in cui è un fattore iniettivo. In seguito, come applicazione della teoria dei sistemi asintoticamente abeliani, si mostra che, se è uno stato vettoriale normale e fedele di , la restrizione...
We prove that the type factor generated by the regular representation of is isomorphic to its tensor product with the hyperfinite type factor. This implies that the unitary group of is contractible with respect to the topology defined by the natural Hilbertian norm.
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,...
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