Elements of a metric spectral theory

Abstract

This paper discusses a general method for spectral type theorems using metric spaces instead of vector spaces. Advantages of this approach are that it applies to genuinely non-linear situations and also to random versions. Metric analogs of operator norm, spectral radius, eigenvalue, linear functional, and weak convergence are suggested. Applications explained include generalizations of the mean ergodic theorem, the Wolff-Denjoy theorem and Thurston's spectral theorem for surface homeomorphisms.

arXiv comment20 pages, 0 figures

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Cited by in corpus (4)

• Characterizing the metric compactification of $L_p$ spaces by random measures
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• Comments on the cosmic convergence of nonexpansive maps