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The generalised Berger-Wang formula and the spectral radius of linear cocycles

Morris, ID (2012) The generalised Berger-Wang formula and the spectral radius of linear cocycles Journal of Functional Analysis, 262 (3). pp. 811-824.

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Using ergodic theory we prove two formulae describing the relationships between different notions of joint spectral radius for sets of bounded linear operators acting on a Banach space. The first formula was previously obtained by V.S. Shulman and Yu.V. Turovskiĭ using operator-theoretic ideas. The second formula shows that the joint spectral radii corresponding to several standard measures of noncompactness share a common value when applied to a given precompact set of operators. This result may be seen as an extension of classical formulae for the essential spectral radius given by R. Nussbaum, A. Lebow and M. Schechter. Both results are obtained as a consequence of a more general theorem concerned with continuous operator cocycles defined over a compact dynamical system. As a byproduct of our method we answer a question of J.E. Cohen on the limiting behaviour of the spectral radius of a measurable matrix cocycle.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Mathematics
Authors :
Date : 2012
DOI : 10.1016/j.jfa.2011.09.021
Depositing User : Symplectic Elements
Date Deposited : 17 May 2017 12:21
Last Modified : 11 Jun 2019 10:10

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