Illinois Journal of Mathematics

Spectral integration from dominated ergodic estimates

Earl Berkson and T. A. Gillespie

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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

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

First available in Project Euclid: 19 October 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42A45: Multipliers
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47A35: Ergodic theory [See also 28Dxx, 37Axx] 47B40: Spectral operators, decomposable operators, well-bounded operators, etc.


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.

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