Doubly power-bounded operators on Lp, 2 ≠ p > 1

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Abstract

We show the existence of a doubly power-bounded T on Lp, 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∈Lp the averages [Formula presented]∑k=1 nTkf (or the averages along the primes or the squares) fail to be a.e. convergent.

Original languageEnglish
Pages (from-to)1327-1336
Number of pages10
JournalJournal of Mathematical Analysis and Applications
Volume466
Issue number2
DOIs
StatePublished - 15 Oct 2018

Keywords

  • Averages along subsequences
  • Doubly power-bounded
  • Lamperti operators
  • Pointwise ergodic theorem
  • Polynomial boundedness
  • Similarity

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