Spectrum for a solvable Lie algebra of operators
Studia Mathematica (1999)
- Volume: 135, Issue: 2, page 163-178
- ISSN: 0039-3223
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topBeltiţă, 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
top- [1] D. W. Barnes, On the cohomology of soluble Lie algebras, Math. Z. 101 (1967), 343-349. Zbl0166.04102
- [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 and A. Larotonda, A spectral theory for solvable Lie algebras of operators, Pacific J. Math. 158 (1993), 15-22. Zbl0789.47004
- [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. Zbl0384.47001
- [6] N. Dunford and J. T. Schwartz, Linear Operators, Part III, Spectral Operators, Interscience, New York, 1971. Zbl0243.47001
- [7] A. S. Fainshtein, Taylor joint spectrum for families of operators generating nilpotent Lie algebras, J. Operator Theory 29 (1993), 3-27. Zbl0859.47005
- [8] Şt. Frunză, The Taylor spectrum and spectral decompositions, J. Funct. Anal. 19 (1975), 390-421. Zbl0306.47013
- [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. Zbl0073.33003
- [13] M. Şabac, Irreducible representations of infinite dimensional Lie algebras, J. Funct. Anal. 52 (1983), 303-314. Zbl0528.17005
- [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. Zbl0306.47014
- [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. Zbl0233.47024
- [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. Zbl0176.30903
- [20] W. Wojtyński, Banach-Lie algebras of compact operators, Studia Math. 59 (1976), 55-65.
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