L² version of Birkhoff: for isometry U on Hilbert space H, the averages (1/n)Σ_{k<n} U^k converge strongly to the orthogonal projection onto {v : Uv = v}. The operator-theoretic kernel of ergodic theory.
L² version of Birkhoff: for isometry U on Hilbert space H, the averages (1/n)Σ_{k<n} U^k converge strongly to the orthogonal projection onto {v : Uv = v}. The operator-theoretic kernel of ergodic theory.