D-sets and a Sárközy Theorem for Countable Fields
نویسنده
چکیده
We establish that if F is a countable field of characteristic p, U is a unitary action of F` on a Hilbert space H , and P is an essential idempotent ultrafilter on F then for every polynomial r : F → F` with r(0) = 0 one has P-limg Ur(g)f = Prf weakly, where Pr is the projection onto the closed subspace Kr = { f ∈ H : {Ur(g)f}g∈F is precompact in the strong topology } . We then derive combinatorial consequences of this result, including results for sufficiently large finite fields.
منابع مشابه
?-Independent and Dissociate Sets on Compact Commutative Strong Hypergroups
In this paper we define ?-independent (a weak-version of independence), Kronecker and dissociate sets on hypergroups and study their properties and relationships among them and some other thin sets such as independent and Sidon sets. These sets have the lacunarity or thinness property and are very useful indeed. For example Varopoulos used the Kronecker sets to prove the Malliavin theorem. In t...
متن کاملCOUNTABLE COMPACTNESS AND THE LINDEL¨OF PROPERTY OF L-FUZZY SETS
In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...
متن کاملIterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings
We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...
متن کاملA countable dense homogeneous set of reals of size א
We prove there is a countable dense homogeneous subspace of R of size א1. The proof involves an absoluteness argument using an extension of the Lω1ω(Q) logic obtained by adding predicates for Borel sets. A separable topological space X is countable dense homogeneous (CDH) if, given any two countable dense subsets D and D′ of X, there is a homeomorphism h of X such that h[D] = D′. The main purpo...
متن کاملNotes on Probability Theory
I Axioms of Probability 2 I-A Set Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A1 Set Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A1a Subsets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 I-A1b Mutually Exclusive Sets or Disjoint Sets . . . . . . . . . . . . . . . . . . . 2...
متن کامل