Positive L¹ operators associated with nonsingular mappings and an example of E. Hille
Isaac Kornfeld, Wojciech Kosek (2003)
Colloquium Mathematicae
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E. Hille [Hi1] gave an example of an operator in L¹[0,1] satisfying the mean ergodic theorem (MET) and such that supₙ||Tⁿ|| = ∞ (actually, ). This was the first example of a non-power bounded mean ergodic L¹ operator. In this note, the possible rates of growth (in n) of the norms of Tⁿ for such operators are studied. We show that, for every γ > 0, there are positive L¹ operators T satisfying the MET with lim supn→ ∞ ||Tⁿ||/n1-γ₀ = 0A class of numerical sequences αₙ, intimately...