Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in
Christophe Cuny (2011)
Colloquium Mathematicae
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We show that some results of Gaposhkin about a.e. convergence of series associated to a unitary operator U acting on L²(X,Σ,μ) (μ is a σ-finite measure) may be extended to the case where U is an invertible power-bounded operator acting on , p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.