Almost everywhere convergence of generalized ergodic transforms for invertible power-bounded operators in $L^{p}$

• Autorzy: Christophe Cuny
• Języki publikacji: EN

Abstrakty

EN

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 $L^{p}(X,Σ,μ)$, p > 1. The proofs make use of the spectral integration initiated by Berkson-Gillespie and, more specifically, of recent results of the author.

Kategorie tematyczne

• 37A30: Ergodic theorems, spectral theory, Markov operators
• 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2011
• Tom: 124
• Numer: 1
• Strony: 61-77

Daty

wydano

2011

Twórcy

autor

Christophe Cuny

• Laboratoire MAS, École Centrale de Paris, Grande Voie des Vignes, 92295 Chatenay-Malabry Cedex, France

Identyfikatory

DOI

10.4064/cm124-1-5