On the joint spectral radius of commuting matrices

Rajendra Bhatia; Tirthankar Вhattacharyya

Studia Mathematica (1995)

  • Volume: 114, Issue: 1, page 29-38
  • ISSN: 0039-3223

Abstract

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For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.

How to cite

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Bhatia, Rajendra, and Вhattacharyya, Tirthankar. "On the joint spectral radius of commuting matrices." Studia Mathematica 114.1 (1995): 29-38. <http://eudml.org/doc/216178>.

@article{Bhatia1995,
abstract = {For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.},
author = {Bhatia, Rajendra, Вhattacharyya, Tirthankar},
journal = {Studia Mathematica},
keywords = {commuting -tuple of matrices; joint spectral radius with respect to the -norm; spectral radius formula},
language = {eng},
number = {1},
pages = {29-38},
title = {On the joint spectral radius of commuting matrices},
url = {http://eudml.org/doc/216178},
volume = {114},
year = {1995},
}

TY - JOUR
AU - Bhatia, Rajendra
AU - Вhattacharyya, Tirthankar
TI - On the joint spectral radius of commuting matrices
JO - Studia Mathematica
PY - 1995
VL - 114
IS - 1
SP - 29
EP - 38
AB - For a commuting n-tuple of matrices we introduce the notion of a joint spectral radius with respect to the p-norm and prove a spectral radius formula.
LA - eng
KW - commuting -tuple of matrices; joint spectral radius with respect to the -norm; spectral radius formula
UR - http://eudml.org/doc/216178
ER -

References

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  1. [BW] M. A. Berger and Y. Wang, Bounded semigroups of matrices, Linear Algebra Appl. 166 (1992), 21-27. Zbl0818.15006
  2. [C1] R. E. Curto, The spectra of elementary operators, Indiana Univ. Math. J. 32 (1983), 193-197. Zbl0488.47002
  3. [C2] R. E. Curto, Applications of several complex variables to multiparameter spectral theory, in: Surveys of Some Recent Results in Operator Theory, Vol. 2, J. B. Conway and B. B. Morrel (eds.), Longman Scientific and Technical, Essex, 1989, 25-80. 
  4. [CH] M. Chō and T. Huruya, On the joint spectral radius, Proc. Roy. Irish Acad. Sect. A 91 (1991), 39-44. Zbl0776.47004
  5. [CZ] M. Chō and W. Żelazko, On geometric spectral radius of commuting n-tuples of operators, Hokkaido Math. J. 21 (1992), 251-258. Zbl0784.47004
  6. [DL] I. Daubechies and J. C. Lagarias, Sets of matrices all finite products of which converge, Linear Algebra Appl. 161 (1992), 227-263. Zbl0746.15015
  7. [E] L. Elsner, The generalized spectral radius theorem, an analytic-geometric proof, Linear Algebra Appl., to appear. Zbl0828.15006
  8. [FN] T. Furuta and R. Nakamoto, On the numerical range of an operator, Proc. Japan Acad. 47 (1971), 279-284. Zbl0227.47002
  9. [HJ] R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge Univ. Press, Cambridge, 1985. 
  10. [MS] V. Müller and A. Sołtysiak, Spectral radius formula for commuting Hilbert space operators, Studia Math. 103 (1992), 329-333. Zbl0812.47004
  11. [P] V. I. Paulsen, Completely Bounded Maps and Dilations, Longman Scientific and Technical, Essex, 1986. 
  12. [R] G. C. Rota, On models for linear operators, Comm. Pure Appl. Math. 13 (1960), 469-472. Zbl0097.31604
  13. [RS] G. C. Rota and W. G. Strang, A note on the joint spectral radius, Indag. Math. 22 (1960), 379-381. Zbl0095.09701

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