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Fall 1999 Spectral integration from dominated ergodic estimates
Earl Berkson, T. A. Gillespie
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Illinois J. Math. 43(3): 500-519 (Fall 1999). DOI: 10.1215/ijm/1255985106

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$\ldots$

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Earl Berkson. T. A. Gillespie. "Spectral integration from dominated ergodic estimates." Illinois J. Math. 43 (3) 500 - 519, Fall 1999. https://doi.org/10.1215/ijm/1255985106

Information

Published: Fall 1999
First available in Project Euclid: 19 October 2009

zbMATH: 0930.42004
MathSciNet: MR1700605
Digital Object Identifier: 10.1215/ijm/1255985106

Subjects:
Primary: 42A45
Secondary: 42B25, 46E30, 47A35, 47B40

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

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Vol.43 • No. 3 • Fall 1999
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