Abstract
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.
Citation
Shigeru Hasegawa. Ryotaro Sato. "On a local ergodic theorem for finite-dimensional-Hilbert-space-valued functions." Tohoku Math. J. (2) 54 (1) 43 - 59, 2002. https://doi.org/10.2748/tmj/1113247178
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