Download PDF - Spectrum for a solvable Lie algebra of operatorsAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Spectrum for a solvable Lie algebra of operators

Authors 1

Affiliations

  1. Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO 70700, Bucureşti, Romania

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.

Bibliography

  1. D. W. Barnes, On the cohomology of soluble Lie algebras, Math. Z. 101 (1967), 343-349.
  2. E. Boasso, Dual properties and joint spectra for solvable Lie algebras of operators, J. Operator Theory 33 (1995), 105-116.
  3. E. Boasso and A. Larotonda, A spectral theory for solvable Lie algebras of operators, Pacific J. Math. 158 (1993), 15-22.
  4. I. Colojoară and C. Foiaş, Theory of Generalized Spectral Operators, Gordon and Breach, New York, 1968.
  5. H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, 1978.
  6. N. Dunford and J. T. Schwartz, Linear Operators, Part III, Spectral Operators, Interscience, New York, 1971.
  7. A. S. Fainshtein, Taylor joint spectrum for families of operators generating nilpotent Lie algebras, J. Operator Theory 29 (1993), 3-27.
  8. Şt. Frunză, The Taylor spectrum and spectral decompositions, J. Funct. Anal. 19 (1975), 390-421.
  9. D. Gurariĭ and Yu. I. Lyubich, An infinite dimensional analogue of Lie's theorem concerning weights, Funktsional. Anal. i Prilozhen. 7 (1973), no. 1, 41-44 (in Russian).
  10. C. Ott, A note on a paper of E. Boasso and A. Larotonda, Pacific J. Math. 173 (1996), 173-180.
  11. —, The Taylor spectrum for solvable operator Lie algebras, preprint, 1996.
  12. M. Rosenblum, On the operator equation BX-XA=Q, Duke Math. J. 23 (1956), 263-269.
  13. M. Şabac, Irreducible representations of infinite dimensional Lie algebras, J. Funct. Anal. 52 (1983), 303-314.
  14. Séminaire Sophus Lie 1954-1955. Théorie des algèbres de Lie. Topologie de groupes de Lie, Paris, Secrétariat mathématique, 1955.
  15. Z. Słodkowski and W. Żelazko, On joint spectra of commuting families of operators, Studia Math. 50 (1974), 127-148.
  16. I. Stewart, Lie Algebras Generated by Finite Dimensional Ideals, Pitman, 1975.
  17. J. L. Taylor, A joint spectrum for several commuting operators, J. Funct. Anal. 6 (1970), 172-191.
  18. F.-H. Vasilescu, Analytic Functional Calculus and Spectral Decompositions, Ed. Academiei and Reidel, Bucharest-Dordrecht, 1982.
  19. D. Winter, Cartan subalgebras of a Lie algebra and its ideals, Pacific J. Math. 33 (1970), 537-541.
  20. W. Wojtyński, Banach-Lie algebras of compact operators, Studia Math. 59 (1976), 55-65.
Studia Mathematica
1999/135/2
Export to PBN, Opens in new tab
Pages:
163-178
Main language of publication
English
Received
1997-05-19
Accepted
1999-02-08
Published
1999
Exact and natural sciences