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Semi-étale groupoids and applications

Klaus Thomsen (2010)

Annales de l’institut Fourier

We associate a C * -algebra to a locally compact Hausdorff groupoid with the property that the range map is locally injective. The construction generalizes J. Renault’s reduced groupoid C * -algebra of an étale groupoid and has the advantage that it works for the groupoid arising from a locally injective dynamical system by the method introduced in increasing generality by Renault, Deaconu and Anantharaman-Delaroche. We study the C * -algebras of such groupoids and give necessary and sufficient conditions...

Square functions, bounded analytic semigroups, and applications

Christian Le Merdy (2007)

Banach Center Publications

To any bounded analytic semigroup on Hilbert space or on L p -space, one may associate natural ’square functions’. In this survey paper, we review old and recent results on these square functions, as well as some extensions to various classes of Banach spaces, including noncommutative L p -spaces, Banach lattices, and their subspaces. We give some applications to H ∞ functional calculus, similarity problems, multiplier theory, and control theory.

Stable outer conjugacy and strong Morita equivalence of group actions on pro-C *-algebras

Maria Joiţa (2009)

Open Mathematics

We show that two continuous inverse limit actions α and β of a locally compact group G on two pro-C *-algebras A and B are stably outer conjugate if and only if there is a full Hilbert A-module E and a continuous action u of G on E such that E and E *(the dual module of E) are countably generated in M(E)(the multiplier module of E), respectively M(E *) and the pair (E, u) implements a strong Morita equivalence between α and β. This is a generalization of a result of F. Combes [Proc. London Math....

Stable rank and real rank of compact transformation group C*-algebras

Robert J. Archbold, Eberhard Kaniuth (2006)

Studia Mathematica

Let (G,X) be a transformation group, where X is a locally compact Hausdorff space and G is a compact group. We investigate the stable rank and the real rank of the transformation group C*-algebra C₀(X)⋊ G. Explicit formulae are given in the case where X and G are second countable and X is locally of finite G-orbit type. As a consequence, we calculate the ranks of the group C*-algebra C*(ℝⁿ ⋊ G), where G is a connected closed subgroup of SO(n) acting on ℝⁿ by rotation.

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