Home Mathematics 15. From Lomonosov lemma to radical approach in joint spectral radius theory
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15. From Lomonosov lemma to radical approach in joint spectral radius theory

  • Edward Kissin , Victor S. Shulman and Yurii V. Turovskii
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Abstract

In this paper, we discuss the infinite-dimensional generalizations of the famous theorem of Berger-Wang (generalized Berger-Wang formulas) and give an operator-theoretic proof of I. Morris’s theorem about coincidence of three essential joint spectral radius, related to these formulas. Further, we develop Banach-algebraic approach based on the theory of topological radicals, and obtain some new results about these radicals.

Abstract

In this paper, we discuss the infinite-dimensional generalizations of the famous theorem of Berger-Wang (generalized Berger-Wang formulas) and give an operator-theoretic proof of I. Morris’s theorem about coincidence of three essential joint spectral radius, related to these formulas. Further, we develop Banach-algebraic approach based on the theory of topological radicals, and obtain some new results about these radicals.

Chapters in this book

  1. Frontmatter I
  2. Editors’ Introduction V
  3. Per Enflo’s personal thoughts about Victor Lomonosov VII
  4. Contents XI
  5. 1. Bishop–Phelps–Bollobás property for positive operators between classical Banach spaces 1
  6. 2. Isometric embeddings of finite metric trees into (ℝn, d1) and (ℝn, d) 15
  7. 3. Iterates of the spherical Aluthge transform of 2-variable weighted shifts 25
  8. 4. The freewheeling twisting of Hilbert spaces 43
  9. 5. A survey of ball-covering property of Banach spaces 67
  10. 6. A note on the quantitative local version of the log-Brunn–Minkowski inequality 85
  11. 7. Spectra of “fattened” open book structures 99
  12. 8. On some local Bishop–Phelps–Bollobás properties 109
  13. 9. Bounded point derivations of fractional orders 123
  14. 10. Invariant subspaces: some minimal proofs 131
  15. 11. On the Hypercyclicity Criterion for operators of Read’s type 139
  16. 12. Three-space problem for strictly convex renormings 149
  17. 13. Norm attaining operators of finite rank 157
  18. 14. Isometric copies of ℓn and ℓn1 in transportation cost spaces on finite metric spaces 189
  19. 15. From Lomonosov lemma to radical approach in joint spectral radius theory 205
  20. 16. Pontryagin–Krein theorem: Lomonosov’s proof and related results 231
  21. 17. Poincaré type and spectral gap inequalities with fractional Laplacians on Hamming cube 251
  22. 18. Spectra of generalized Poisson integral operators on Lp(ℝ+) 281
  23. 19. Order extreme points and solid convex hulls 297
  24. 20. Universal block tridiagonalization in ℬ(ℋ) and beyond 317
  25. 21. Rademacher-type independence in Boolean algebras 327
  26. Index 349
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