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On positive unipotent operators on Banach lattices

Author(s): Roman Drnovsek
Journal: Proc. Amer. Math. Soc. 135 (2007), 3833-3836.
MSC (2000): Primary 47B65, 47A10
Posted: August 17, 2007
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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: 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
Posted: 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 of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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