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The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present a condition implying that every affine isometric action of a given group $G$ on a reflexive Banach space $X$ has a fixed point. This last property is a strong version of Kazhdan’s property (T) and is equivalent to the fact that $H^{1} (G, π) = 0$ for every isometric representation $π$ of $G$ on $X$ . The condition is expressed in terms of $p$ -Poincaré constants and we provide examples...

p-Pseudomeasures and Closed Subgroups.

A. Derighetti, J. Delaporte (1995)

Monatshefte für Mathematik

Représentation non linéaire du groupe affine complexe

Abdelwaheb Charfi (1991)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Représentations approchées d'un groupe dans un algèbre de Banach.

P. de de Harpe, Max Karoubi (1977)

Manuscripta mathematica

Représentations de $G^{X}$ (G compact) selon Verchik-Gelfand-Graiev et Ismagilov

Alain Guichardet (1978/1979)

Séminaire Bourbaki

Représentations intégrales dans les cônes convexes conucléaires et applications

Erik G. F. Thomas (1977)

Séminaire Choquet. Initiation à l'analyse

Representations of Polish groups and continuity

M. Cianfarani, J.-M. Paoli, P. Simonnet, J.-C. Tomasi (2014)

Studia Mathematica

In the first part of the paper, some criteria of continuity of representations of a Polish group in a Banach algebra are given. The second part uses the result of the first part to deduce automatic continuity results of Baire morphisms from Polish groups to locally compact groups or unitary groups. In the final part, the spectrum of an element in the range of a strongly but not norm continuous representation is described.

Some Remarks on Automorphisms of Bounded Displacement and Bounded Cocycles.

Martin Moskowitz (1978)

Monatshefte für Mathematik

Spherical functions and uniformly bounded representations of free groups

Tadeusz Pytlik (1991)

Studia Mathematica

We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.

Square integrability of group representations on homogeneous spaces. II. Coherent and quasi-coherent states. The case of the Poincaré group

S. T. Ali, J.-P. Antoine, J.-P. Gazeau (1991)

Annales de l'I.H.P. Physique théorique

Square integrability of group representations on homogeneous spaces. I. Reproducing triples and frames

S. T. Ali, J.-P. Antoine, J.-P. Gazeau (1991)

Annales de l'I.H.P. Physique théorique

Square-integrability of tensor products.

Mayer, Matthias (1999)

Journal of Lie Theory

Tensor products and p-induction of representations on Banach spaces.

Philippe Jaming, William Moran (2000)

Collectanea Mathematica

In this paper we obtain Lp versions of the classical theorems of induced representations, namely, the inducing in stages theorem, the Kronecker product theorem, the Frobenius Reciprocity theorem and the subgroup theorem. In doing so we adopt the tensor product approach of Rieffel to inducing.

Über die Wiener-Eigenschaft bei projektiven Limites lokalkompakter Gruppen.

Bernhard Heß (1977)

Manuscripta mathematica

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