1 - 10 of 13 articles
By regarding the classical non-abelian cohomology of groups from a 2-dimensional categorical viewpoint, we are led to a non-abelian cohomology of groupoids which continues to satisfy classification, interpretation and representation theorems generalizing the classical ones. This categorical...
Let H and Γ be two discrete groups and X be a set on which Γ acts. We investigate when the wreath product H≀
Γ has relative property (T) and give a complete characterization of property (T) for such groups. Moreover we determine a lower bound of a Kazhdan constant for H≀
Γ in terms of those...
We present a theory of quantum (non-commutative) Lévy processes on dual groups which generalizes the theory of Lévy processes on bialgebras. It follows from a result of N. Muraki that there exist exactly 5 notions of non-commutative ‘positive’ stochastic independence. We show that one can...
Let X be a (closed) subspace of L
with 1≤p<∞, and let A be any sectorial operator on X. We consider associated square functions on X, of the form [InlineMediaObject not available: see fulltext.] and we show that if A admits a bounded H
∞ functional calculus on X, then these square functions...
Slope inequalities are given for fibred rational surfaces according as the Clifford index of a general fibre. For fibred rational surfaces of Clifford index two, the Mordell-Weil lattices of maximal ranks are completely determined.
In the setting of doubling metric measure spaces with a 1-Poincaré inequality, we show that sets of Orlicz Φ-capacity zero have generalized Hausdorff h-measure zero provided that
The main result of this paper is a lower bound for the essential spectrum of Schrödinger operators −Δ+V on Riemannian manifolds. In particular, we obtain conditions on V which imply the discreteness of the spectrum, or equivalently, the compactness of the resolvent.
It is shown that the product of two sectorial operators A and B admits a bounded H
∞-calculus on a Banach space X provided suitable commutator estimates and Kalton-Weis type assumptions on A and B are satisfied.
Abstract For any simply connected solvable Lie group Q of polynomial volume growth, we introduce the notion of nil-shadow of Q. We shall give an explicit formula for the distance to the origin of an element q ∈ Q in terms of its exponential coordinates of the second kind taken in an appropriate...
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