Abstract
The paper introduces a new type of grand Lebesgue space, for which special cases are weighted grand Lebesgue spaces introduced by Fiorenza, Gupta and Jain (2008) and a generalization of grand Lebesgue spaces introduced by Greco, Iwaniec and Sbordone (1997). The main result is a mean ergodic theorem, in the Von Neumann sense, for some operator acting on the closure of the set of compactly supported in the newly introduced grand Lebesgue space.
Cuvinte cheie
Mean ergodic theorem
Iwaniec-Sbordone space
weighted Lebesgue spaces
averages of iterates