James Hogan Department of Mathematics, University of Toronto, 40 St George St, Toronto, ON M5S 2E4
e-mail: james.hogan@mail.utoronto.ca

Samuel Li Department of Mathematics, University of Toronto, 40 St George St, Toronto, ON M5S 2E4
e-mail: samuelj.li@mail.utoronto.ca

Abstract/Résumé:

We highlight the surprising power of averaging via a few illuminating examples. Two of these problems involve characterizations of Hilbert space, and the third is a fundamental result in noncommutative geometry.

Nous soulignons le pouvoir surprenant de la moyenne par quelques exemples éclairants. Deux de ces problèmes concernent la caractérisation de l’espace de Hilbert, et le troisième est un résultat fondamental en géométrie non commutative.

Keywords: Averaging, Hilbert space, Irrational rotation algebra, noncommutative geometry

AMS Subject Classification: Instructional exposition (textbooks; tutorial papers; etc.), Characterizations of Hilbert spaces, Noncommutative geometry (__ la Connes) 00-01, 46C15, 58B34

PDF(click to download): The Surprising Power of Averaging over Groups