On the joint spectral radius of a nilpotent Lie algebra of matrices

Enrico Boasso

Studia Mathematica (1999)

  • Volume: 132, Issue: 1, page 15-27
  • ISSN: 0039-3223

Abstract

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For a complex nilpotent finite-dimensional Lie algebra of matrices, and a Jordan-Hölder basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.

How to cite

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Boasso, Enrico. "On the joint spectral radius of a nilpotent Lie algebra of matrices." Studia Mathematica 132.1 (1999): 15-27. <http://eudml.org/doc/216582>.

@article{Boasso1999,
abstract = {For a complex nilpotent finite-dimensional Lie algebra of matrices, and a Jordan-Hölder basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.},
author = {Boasso, Enrico},
journal = {Studia Mathematica},
keywords = {Taylor spectrum; joint spectral radius; nilpotent Lie algebras; Lie algebra of matrices; Jordan-Hölder basis},
language = {eng},
number = {1},
pages = {15-27},
title = {On the joint spectral radius of a nilpotent Lie algebra of matrices},
url = {http://eudml.org/doc/216582},
volume = {132},
year = {1999},
}

TY - JOUR
AU - Boasso, Enrico
TI - On the joint spectral radius of a nilpotent Lie algebra of matrices
JO - Studia Mathematica
PY - 1999
VL - 132
IS - 1
SP - 15
EP - 27
AB - For a complex nilpotent finite-dimensional Lie algebra of matrices, and a Jordan-Hölder basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.
LA - eng
KW - Taylor spectrum; joint spectral radius; nilpotent Lie algebras; Lie algebra of matrices; Jordan-Hölder basis
UR - http://eudml.org/doc/216582
ER -

References

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  1. [1] R. Bhatia and T. Bhattacharyya, On the joint spectral radius of commuting matrices, Studia Math. 114 (1995), 29-38. Zbl0830.47002
  2. [2] E. Boasso, Dual properties and joint spectra for solvable Lie algebras of operators, J. Operator Theory 33 (1995), 105-116. Zbl0838.47036
  3. [3] E. Boasso, Joint spectra and nilpotent Lie algebras of Linear transformations, Linear Algebra Appl. 263 (1997), 49-62. Zbl0965.47004
  4. [4] E. Boasso and A. Larotonda, A spectral theory for solvable Lie algebras of operators, Pacific J. Math. 158 (1993), 15-22. Zbl0789.47004
  5. [5] N. Bourbaki, Éléments de Mathématique, Groupes et Algèbres de Lie, Algèbres de Lie Fasc. XXVI, Hermann, 1960. Zbl0199.35203
  6. [6] M. Chō and T. Huruya, On the joint spectral radius, Proc. Roy. Irish Acad. Sect. A 91 (1991), 39-44. Zbl0776.47004
  7. [7] M. Chō and M. Takaguchi, Identity of Taylor's joint spectrum and Dash's joint spectrum, Studia Math. 70 (1982), 225-229. Zbl0494.47003
  8. [8] N. Jacobson, Lie Algebras, Interscience Publ., 1962. 
  9. [9] A. McIntosh, A. Pryde and W. Ricker, Comparison of joint spectra for certain classes of commuting opertors, Studia Math. 88 (1988), 23-36. Zbl0665.47002
  10. [10] C. Ott, A note on a paper of E. Boasso and A. Larotonda, Pacific J. Math. 173 (1996), 173-179. 
  11. [11] Z. Słodkowski, An infinite family of joint spectra, Studia Math. 61 (1973), 239-235. Zbl0369.47021
  12. [12] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191. Zbl0233.47024

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