We establish new connections between some classes of lacunary sets. The main tool is the use of (p,q)-summing or weakly compact operators (for Riesz sets). This point of view provides new properties of stationary sets and allows us to generalize to more general abelian groups than the torus some properties of p-Sidon sets. We also construct some new classes of Riesz sets.
On associe à certaines suites de nombres complexes une mesure borélienne positive sur le tore dont la transformée de Fourier-Walsh est une suite de moyennes liées à . La nature de (discrète, continue) est discutée dans quelques cas : suites presque-périodiques et certaines suites arithmétiques.
We investigate several aspects of almost 1-unconditionality. We characterize the metric unconditional approximation property (umap) in terms of “block unconditionality”. Then we focus on translation invariant subspaces and of functions on the circle and express block unconditionality as arithmetical conditions on E. Our work shows that the spaces , p an even integer, have a singular behaviour from the almost isometric point of view: property (umap) does not interpolate between and . These...
We first study the behavior of weights on a simply connected nilpotent Lie group G. Then for a subalgebra A of L¹(G) containing the Schwartz algebra 𝓢(G) as a dense subspace, we characterize all closed two-sided ideals of A whose hull reduces to one point which is a character.
Let be an -algebraic semisimple group, an algebraic -subgroup, and a lattice in . Partially answering a question posed by Hillel Furstenberg in 1972, we prove that if the action of on is minimal, then it is uniquely ergodic. Our proof uses in an essential way Marina Ratner’s classification of probability measures on invariant under unipotent elements, and the study of “tubes” in .
A semigroup in , a Banach space, is called mean ergodic, if its closed convex hull in has a zero element. Compact groups, compact abelian semigroups or contractive semigroups on Hilbert spaces are mean ergodic.Banach lattices prove to be a natural frame for further mean ergodic theorems: let be a bounded semigroup of positive operators on a Banach lattice with order continuous norm. is mean ergodic if there is a -subinvariant quasi-interior point of and a -subinvariant strictly...