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

Author:
Guy Cohen  


Journal:
Journal of Mathematical Analysis and Applications


Issue Date:
2018


Abstract(summary):

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 kf (or the averages along the primes or the squares) fail to be a.e. convergent.


Page:
1327-1327


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