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Group C*-algebras satisfying Kadison's conjecture

Rachid El Harti, Paulo R. Pinto (2011)

Banach Center Publications

We tackle R. V. Kadison’s similarity problem (i.e. any bounded representation of any unital C*-algebra is similar to a *-representation), paying attention to the class of C*-unitarisable groups (those groups G for which the full group C*-algebra C*(G) satisfies Kadison’s problem) and thereby we establish some stability results for Kadison’s problem. Namely, we prove that A m i n B inherits the similarity problem from those of the C*-algebras A and B, provided B is also nuclear. Then we prove that G/Γ is...

Groupes fondamentaux des variétés de dimension 3 et algèbres d’opérateurs

Pierre de la Harpe, Jean-Philippe Préaux (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

Nous proposons une caractérisation géométrique des variétés de dimension  3 ayant des groupes fondamentaux dont toutes les classes de conjugaison autres que  { 1 } sont infinies, c’est-à-dire dont les algèbres de von Neumann sont des facteurs de type  I I 1   : ce sont essentiellement les 3 -variétés à groupes fondamentaux infinis qui n’admettent pas de fibration de Seifert. Autrement dit et plus précisément, soient  M une 3 -variété connexe compacte et Γ son groupe fondamental, qu’on suppose être infini et avec...

Growth and smooth spectral synthesis in the Fourier algebras of Lie groups

Jean Ludwig, Lyudmila Turowska (2006)

Studia Mathematica

Let G be a Lie group and A(G) the Fourier algebra of G. We describe sufficient conditions for complex-valued functions to operate on elements u ∈ A(G) of certain differentiability classes in terms of the dimension of the group G. Furthermore, generalizing a result of Kirsch and Müller [Ark. Mat. 18 (1980), 145-155] we prove that closed subsets E of a smooth m-dimensional submanifold of a Lie group G having a certain cone property are sets of smooth spectral synthesis. For such sets we give an estimate...

Growth of coefficients of universal Dirichlet series

A. Mouze (2007)

Annales Polonici Mathematici

We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.

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