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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… Click to show full abstract
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.
Keywords:
bounded operators;
power bounded;
doubly power;
operator
Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
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Journal Title: Journal of Mathematical Analysis and Applications
Year Published: 2018
Link to full text (if available)
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recommendations!