Doubly power-bounded operators on L, 2 ≠ p > 1 Academic Article uri icon

abstract

  • We show the existence of a doubly power-bounded T on L p , 1 p ∞ , p ≠ 2 , such that T is spectral of scalar type (hence polynomially bounded), T is not similar to a Lamperti operator (hence is not similar to an isometry), none of the powers of T is similar to a Lamperti operator, none of the powers is similar to a positive operator, and for some f ∈ L p the averages 1 n ∑ k = 1 n T k f (or the averages along the primes or the squares) fail to be a.e. convergent.

publication date

  • October 1, 2018