A Polish AR-Space with no Nontrivial Isotopy
The Polish space Y constructed in [vM1] admits no nontrivial isotopy. Yet, there exists a Polish group that acts transitively on Y.
A Proof of Blattner's Conjecture.
A proof of the Mackey-Blattner-Nielsen theorem.
A property for locally convex *-algebras related to property (T) and character amenability
For a locally convex *-algebra A equipped with a fixed continuous *-character ε (which is roughly speaking a generalized F*-algebra), we define a cohomological property, called property (FH), which is similar to character amenability. Let be the space of continuous functions with compact support on a second countable locally compact group G equipped with the convolution *-algebra structure and a certain inductive topology. We show that has property (FH) if and only if G has property (T). On...
À propos de l'article «Sur la cohomologie réelle des groupes de Lie simples réels»
À propos des convoluteurs d'un groupe quotient
A Qualitative Uncertainty Principle for Certain Locally Compact Groups.
A quest for nice kernels of neighbourhood assignments
Given a topological property (or a class) , the class dual to (with respect to neighbourhood assignments) consists of spaces such that for any neighbourhood assignment there is with and . The spaces from are called dually . We continue the study of this duality which constitutes a development of an idea of E. van Douwen used to define -spaces. We prove a number of results on duals of some general classes of spaces establishing, in particular, that any generalized ordered space...
A ratio ergodic theorem for multiparameter non-singular actions
We prove a ratio ergodic theorem for non-singular free and actions, along balls in an arbitrary norm. Using a Chacon–Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in . The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact that boundaries of balls have lower dimension than the ambient space. We also show that for general group...
A reconstruction theorem for locally moving groups acting on completely metrizable spaces
Let G be a group which acts by homeomorphisms on a metric space X. We say the action of G is locally moving on X if for every open U ⊆ X there is a g ∈ G such that g↾X ≠ Id while g↾(X∖U) = Id. We prove the following theorem: Theorem A. Let X,Y be completely metrizable spaces and let G be a group which acts on X and Y with locally moving actions. If the orbits of the action of G on X are of the second category in X and the orbits of the action of G on Y are of the second category...
A recurrence relation approach to higher order quantum superintegrability.
A relation between automorphic representations of and
A relative trace formula
A relatively free topological group that is not varietal free
Answering a 1982 question of Sidney A. Morris, we construct a topological group G and a subspace X such that (i) G is algebraically free over X, (ii) G is relatively free over X, that is, every continuous mapping from X to G extends to a unique continuous endomorphism of G, and (iii) G is not a varietal free topological group on X in any variety of topological groups.
A remark on a Marcinkiewicz-Hörmander multiplier theorem for some non-differential convolution operators
A remark on a theorem of R. S. Irving and L. W. Small. (Une remarque sur un théorème de R. S. Irving et L. W. Small.)
A remark on compact semi lattices of groups.
A Remark on Discontinuous Translation Invariant Functionals on L... (G) for Certain Compact Groups G.
A Remark on Invariant Pseudo-Differential Operators.
A remark on my paper "On the Saito-Kurokawa lifting".