Spectrum for a solvable Lie algebra of operators
Studia Mathematica (1999)
- Volume: 135, Issue: 2, page 163-178
- ISSN: 0039-3223
Access Full Article
topAbstract
topHow to cite
topReferences
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.