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

 

Ideal-triangularizability of nil-algebras generated by positive operators


Author: Marko Kandić
Journal: Proc. Amer. Math. Soc. 139 (2011), 485-490
MSC (2010): Primary 47A15, 47B65; Secondary 16N40
Published electronically: July 12, 2010
MathSciNet review: 2736331
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Abstract: R. Drnovšek, D. Kokol-Bukovšek, L. Livshits, G. MacDonald, M. Omladič, and H. Radjavi constructed an irreducible set of positive nilpotent operators on $ L^p[0,1)$ which is closed under multiplication, addition and multiplication by positive real scalars with the property that any finite subset is ideal-triangularizable. In this paper we prove the following:

  1. every algebra of nilpotent operators which is generated by a set of positive operators on a Banach lattice is ideal-triangularizable whenever the nilpotency index of its operators is bounded;
  2. every finite subset of an algebra of nilpotent operators which is generated by a set of positive operators on a Banach lattice is ideal-triangularizable.


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Additional Information

Marko Kandić
Affiliation: Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Email: marko.kandic@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10476-8
PII: S 0002-9939(2010)10476-8
Keywords: Banach lattices, positive operators, operator semigroups, ideal-reducibility, ideal-triangularizability, nilpotent algebras, nil-algebras
Received by editor(s): December 17, 2009
Received by editor(s) in revised form: March 2, 2010
Published electronically: July 12, 2010
Additional Notes: This work was supported by the Slovenian Research Agency
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.