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On the Joint Spectral Radius

In: Analysis at Large

Author

Listed:
  • Emmanuel Breuillard

    (University of Cambridge, DPMMS)

Abstract

For a bounded subset S of d × d complex matrices, the Berger-Wang theorem and Bochi’s inequality allow to approximate the joint spectral radius of S from below by the spectral radius of a short product of elements from S. Our goal is twofold: we review these results, providing self-contained proofs, and we derive an improved version with explicit bounds that are polynomial in d. We also discuss other complete valued fields.

Suggested Citation

  • Emmanuel Breuillard, 2022. "On the Joint Spectral Radius," Springer Books, in: Artur Avila & Michael Th. Rassias & Yakov Sinai (ed.), Analysis at Large, pages 1-16, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-05331-3_1
    DOI: 10.1007/978-3-031-05331-3_1
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