## Illinois Journal of Mathematics

### Spectral integration from dominated ergodic estimates

#### Abstract

Suppose that $(\Omega,\mathcal{M},\mu)$ is a $\sigma$-finite measure space, $1 \lt p \lt \infty$, and $T: L^{p}(\mu) \rightarrow L^{p}(\mu)$ is a bounded, invertible, separation-preserving linear operator such that the two-sided ergodic means of the linear modulus of $T$ are uniformly bounded in norm. Using the spectral structure of $T$, we obtain a functional calculus for $T$ associated with the algebra of Marcinkiewicz multipliers defined on the unit circle$\ldots$

#### Article information

Source
Illinois J. Math., Volume 43, Issue 3 (1999), 500-519.

Dates
First available in Project Euclid: 19 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1255985106

Digital Object Identifier
doi:10.1215/ijm/1255985106

Mathematical Reviews number (MathSciNet)
MR1700605

Zentralblatt MATH identifier
0930.42004

#### Citation

Berkson, Earl; Gillespie, T. A. Spectral integration from dominated ergodic estimates. Illinois J. Math. 43 (1999), no. 3, 500--519. doi:10.1215/ijm/1255985106. https://projecteuclid.org/euclid.ijm/1255985106