Invariant subspaces of super left-commutants
HTML articles powered by AMS MathViewer
- by Hailegebriel E. Gessesse
- Proc. Amer. Math. Soc. 137 (2009), 1357-1361
- DOI: https://doi.org/10.1090/S0002-9939-08-09673-1
- Published electronically: October 6, 2008
- PDF | Request permission
Abstract:
For a positive operator $Q$ on a Banach lattice, one defines $\langle Q]=\{T\geq 0 : ~TQ\leq QT\}$ and $[Q\rangle =\{T\geq 0 : TQ\geq QT\}$. There have been several recent results asserting that, under certain assumptions on $Q$, $[Q\rangle$ has a common invariant subspace. In this paper, we use the technique of minimal vectors to establish similar results for $\langle Q]$.References
- Y. A. Abramovich and C. D. Aliprantis, An invitation to operator theory, Graduate Studies in Mathematics, vol. 50, American Mathematical Society, Providence, RI, 2002. MR 1921782, DOI 10.1090/gsm/050
- Charalambos D. Aliprantis and Owen Burkinshaw, Positive operators, Pure and Applied Mathematics, vol. 119, Academic Press, Inc., Orlando, FL, 1985. MR 809372
- Razvan Anisca and Vladimir G. Troitsky, Minimal vectors of positive operators, Indiana Univ. Math. J. 54 (2005), no. 3, 861–872. MR 2151236, DOI 10.1512/iumj.2005.54.2544
- Shamim Ansari and Per Enflo, Extremal vectors and invariant subspaces, Trans. Amer. Math. Soc. 350 (1998), no. 2, 539–558. MR 1407476, DOI 10.1090/S0002-9947-98-01865-0
- Roman Drnovšek, Common invariant subspaces for collections of operators, Integral Equations Operator Theory 39 (2001), no. 3, 253–266. MR 1818060, DOI 10.1007/BF01332655
- J. Flores, P. Tradacete and V. G. Troitsky, Invariant subspaces of positive strictly singular operators on Banach lattices, J. Math. Anal. Appl., 343, 2008, 743-751.
- H. Gessesse and V. G. Troitsky, Invariant subspaces of positive quasinilpotent operators on ordered Banach spaces, Positivity, 12, 2008, 193–208.
- Vladimir G. Troitsky, Minimal vectors in arbitrary Banach spaces, Proc. Amer. Math. Soc. 132 (2004), no. 4, 1177–1180. MR 2045435, DOI 10.1090/S0002-9939-03-07223-X
Bibliographic Information
- Hailegebriel E. Gessesse
- Affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, T6G 2G1, Canada
- Email: hgessesse@math.ualberta.ca
- Received by editor(s): April 11, 2008
- Published electronically: October 6, 2008
- Communicated by: Nigel J. Kalton
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 1357-1361
- MSC (2000): Primary 47A15; Secondary 46B42, 47B65
- DOI: https://doi.org/10.1090/S0002-9939-08-09673-1
- MathSciNet review: 2465659