On positive unipotent operators on Banach lattices
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Abstract:
Let $T$ be a positive operator on a complex Banach lattice. We prove that $T$ is greater than or equal to the identity operator $I$ if \[ \lim _{n \rightarrow \infty } n \|(T - I)^n\|^{1/n} = 0. \]References
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Additional Information
- Roman Drnovšek
- Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19. SI-1000 Ljubljana, Slovenia
- Email: Roman.Drnovsek@fmf.uni-lj.si
- Received by editor(s): December 1, 2005
- Received by editor(s) in revised form: August 23, 2006
- Published electronically: August 17, 2007
- Additional Notes: This work was supported in part by the Ministry of Higher Education, Science and Technology of Slovenia.
- Communicated by: Joseph A. Ball
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 3833-3836
- MSC (2000): Primary 47B65, 47A10
- DOI: https://doi.org/10.1090/S0002-9939-07-08907-1
- MathSciNet review: 2341933