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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On positive unipotent operators on Banach lattices


Author: Roman Drnovsek
Journal: Proc. Amer. Math. Soc. 135 (2007), 3833-3836
MSC (2000): Primary 47B65, 47A10
Published electronically: August 17, 2007
MathSciNet review: 2341933
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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

$\displaystyle \lim_{n \rightarrow \infty} n \, \Vert(T - I)^n\Vert^{1/n} = 0. $


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Additional Information

Roman Drnovsek
Affiliation: Department of Mathematics, University of Ljubljana, Jadranska 19. SI-1000 Ljubljana, Slovenia
Email: Roman.Drnovsek@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08907-1
PII: S 0002-9939(07)08907-1
Keywords: Banach lattices, positive operators, spectrum
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
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.