We consider a Banach space of finite-dimensional-Hilbert-space-valued functions on a sigma-finite measure space. The norm of the function space is assumed to satisfy some suitable conditions. Then we prove a pointwise local ergodic theorem for a $(C_{0})$-semigroup of linear contractions on the function space, under an additional norm condition for operators of the semigroup. Our result extends Baxter and Chacon's local ergodic theorem for scalar-valued functions.
Publié le : 2002-03-14
Classification:
Pointwise local ergodic theorem,
$(C_{0})$-semigroup of linear contractions,
Banach space of finite-dimensional-Hilbert-space-valued functions,
47A35,
47D06
@article{1113247178,
author = {Hasegawa, Shigeru and Sato, Ryotaro},
title = {On a local ergodic theorem for finite-dimensional-Hilbert-space-valued functions},
journal = {Tohoku Math. J. (2)},
volume = {54},
number = {1},
year = {2002},
pages = { 43-59},
language = {en},
url = {http://dml.mathdoc.fr/item/1113247178}
}
Hasegawa, Shigeru; Sato, Ryotaro. On a local ergodic theorem for finite-dimensional-Hilbert-space-valued functions. Tohoku Math. J. (2), Tome 54 (2002) no. 1, pp. 43-59. http://gdmltest.u-ga.fr/item/1113247178/