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.
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تاریخ انتشار 2012