Spectrum for a solvable Lie algebra of operators

Daniel Beltiţă

Studia Mathematica (1999)

  • Volume: 135, Issue: 2, page 163-178
  • ISSN: 0039-3223

Abstract

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A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.

How to cite

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Beltiţă, Daniel. "Spectrum for a solvable Lie algebra of operators." Studia Mathematica 135.2 (1999): 163-178. <http://eudml.org/doc/216648>.

@article{Beltiţă1999,
abstract = {A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.},
author = {Beltiţă, Daniel},
journal = {Studia Mathematica},
keywords = {solvable Lie algebra; joint spectrum; nilpotent Lie algebra; Cartan decompositions; Riesz-Schauder theory},
language = {eng},
number = {2},
pages = {163-178},
title = {Spectrum for a solvable Lie algebra of operators},
url = {http://eudml.org/doc/216648},
volume = {135},
year = {1999},
}

TY - JOUR
AU - Beltiţă, Daniel
TI - Spectrum for a solvable Lie algebra of operators
JO - Studia Mathematica
PY - 1999
VL - 135
IS - 2
SP - 163
EP - 178
AB - A new concept of spectrum for a solvable Lie algebra of operators is introduced, extending the Taylor spectrum for commuting tuples. This spectrum has the projection property on any Lie subalgebra and, for algebras of compact operators, it may be computed by means of a variant of the classical Ringrose theorem.
LA - eng
KW - solvable Lie algebra; joint spectrum; nilpotent Lie algebra; Cartan decompositions; Riesz-Schauder theory
UR - http://eudml.org/doc/216648
ER -

References

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  3. [3] E. Boasso and A. Larotonda, A spectral theory for solvable Lie algebras of operators, Pacific J. Math. 158 (1993), 15-22. Zbl0789.47004
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  10. [10] C. Ott, A note on a paper of E. Boasso and A. Larotonda, Pacific J. Math. 173 (1996), 173-180. 
  11. [11] —, The Taylor spectrum for solvable operator Lie algebras, preprint, 1996. 
  12. [12] M. Rosenblum, On the operator equation BX-XA=Q, Duke Math. J. 23 (1956), 263-269. Zbl0073.33003
  13. [13] M. Şabac, Irreducible representations of infinite dimensional Lie algebras, J. Funct. Anal. 52 (1983), 303-314. Zbl0528.17005
  14. [14] Séminaire Sophus Lie 1954-1955. Théorie des algèbres de Lie. Topologie de groupes de Lie, Paris, Secrétariat mathématique, 1955. 
  15. [15] Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148. Zbl0306.47014
  16. [16] I. Stewart, Lie Algebras Generated by Finite Dimensional Ideals, Pitman, 1975. 
  17. [17] J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191. Zbl0233.47024
  18. [18] F.-H. Vasilescu, Analytic Functional Calculus and Spectral Decompositions, Ed. Academiei and Reidel, Bucharest-Dordrecht, 1982. 
  19. [19] D. Winter, Cartan subalgebras of a Lie algebra and its ideals, Pacific J. Math. 33 (1970), 537-541. Zbl0176.30903
  20. [20] W. Wojtyński, Banach-Lie algebras of compact operators, Studia Math. 59 (1976), 55-65. 

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