arXiv subjects
Publications and source records attributed to Rafael Zamora.
We establish new strong factorization properties for the smooth vectors of representations of exponential solvable Lie groups on Fréchet spaces. In particular, our results improve upon the Dixmier-Malliavin factorization theorem for simply connected nilpotent Lie groups.
We study global dynamical properties of the isometry group of the Borel randomization of a separable complete structure. In particular, we show that if properties such as the Rohklin property, topometric generics, extreme amenability hold for the isometry group of the structure, they also hold in the isometry group of the randomization.
We prove an analogue of the fixed-point theorem for the case of definably amenable groups.
We study injective versions of the characterization of sets potentially in a Wadge class of Borel sets, for the first Borel and Lavrentieff classes. We also study the case of oriented graphs in terms of continuous homomorphisms, injective or not.
We provide Hurewicz tests for the separation of disjoint analytic sets by rectangles of the form $Γ\timesΓ'$ for $Γ,Γ'\in {\mathbfΣ^0_1 , \mathbfΠ^0_1 , \mathbfΠ^0_2 }$.