Model theory and metric convergence II: Averages of unitary polynomial actions
| Autor: | José Iovino, Eduardo Dueñez |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0301 basic medicine
Polynomial (hyperelastic model) Pointwise convergence Hilbert space 16. Peace & justice Unitary state Combinatorics 03 medical and health sciences symbols.namesake Lamplighter group 030104 developmental biology symbols Unitary operator Abelian group Polynomial sequence Mathematics |
| Zdroj: | Mexican Mathematicians in the World. :85-114 |
| ISSN: | 1098-3627 0271-4132 |
| DOI: | 10.1090/conm/775/15590 |
| Popis: | We use model theory of metric structures to prove the pointwise convergence, with a uniform metastability rate, of averages of a polynomial sequence { T n } \{T_n\} (in Leibman’s sense) of unitary transformations of a Hilbert space. As a special case, this applies to unitary sequences { U p ( n ) } \{U^{p(n)}\} where p p is a polynomial Z → Z \mathbb {Z}\to \mathbb {Z} and U U a fixed unitary operator; however, our convergence results hold for arbitrary Leibman sequences. As a case study, we show that the non-nilpotent “lamplighter group” Z ≀ Z \mathbb {Z}\wr \mathbb {Z} is realized as the range of a suitable quadratic Leibman sequence. We also indicate how these convergence results generalize to arbitrary Følner averages of unitary polynomial actions of any abelian group G \mathbb {G} in place of Z \mathbb {Z} . |
| Databáze: | OpenAIRE |
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