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

Studia Mathematica (1999)

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

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topBoasso, 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

top- [1] R. Bhatia and T. Bhattacharyya, On the joint spectral radius of commuting matrices, Studia Math. 114 (1995), 29-38. Zbl0830.47002
- [2] E. Boasso, Dual properties and joint spectra for solvable Lie algebras of operators, J. Operator Theory 33 (1995), 105-116. Zbl0838.47036
- [3] E. Boasso, Joint spectra and nilpotent Lie algebras of Linear transformations, Linear Algebra Appl. 263 (1997), 49-62. Zbl0965.47004
- [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] N. Bourbaki, Éléments de Mathématique, Groupes et Algèbres de Lie, Algèbres de Lie Fasc. XXVI, Hermann, 1960. Zbl0199.35203
- [6] M. Chō and T. Huruya, On the joint spectral radius, Proc. Roy. Irish Acad. Sect. A 91 (1991), 39-44. Zbl0776.47004
- [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] N. Jacobson, Lie Algebras, Interscience Publ., 1962.
- [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] C. Ott, A note on a paper of E. Boasso and A. Larotonda, Pacific J. Math. 173 (1996), 173-179.
- [11] Z. Słodkowski, An infinite family of joint spectra, Studia Math. 61 (1973), 239-235. Zbl0369.47021
- [12] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191. Zbl0233.47024

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