Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

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
MathSciNet review: 2341933
Retrieve article in: PDF

Abstract | References | Similar articles | Additional information

Abstract: Let be a positive operator on a complex Banach lattice. We prove that is greater than or equal to the identity operator if

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

References:

1.: C.D. Aliprantis, O. Burkinshaw, Positive operators, Academic Press, Orlando 1985. MR 809372 (87h:47086)
2.: B. Ya. Levin, Lectures on entire functions, Translations of Mathematical Monographs 150, American Mathematical Society, Providence, 1996. MR 1400006 (97j:30001)
3.: W. A. J. Luxemburg, B. de Pagter, A. R. Schep, Diagonals of the powers of an operator on a Banach lattice, in: Operator theory in function spaces and Banach lattices, 223-273, Oper. Theory Adv. Appl. 75, Birkhäuser, Basel, 1995. MR 1322506 (97i:47076)
4.: P. Meyer-Nieberg, Banach lattices, Springer-Verlag, Berlin, 1991. MR 1128093 (93f:46025)
5.: S. Mouton, A spectral problem in ordered Banach algebras, Bull. Austral. Math. Soc. 67 (2003), no. 1, 131-144. MR 1962967 (2004d:47075)
6.: B. de Pagter, Irreducible compact operators, Math. Z. 192 (1986), 149-153. MR 835399 (87d:47052)
7.: H.H. Schaefer, Topologische Nilpotenz irreduzibler Operatoren, Math. Z. 117 (1970), 135-140. MR 0276802 (43:2542)
8.: J. Voigt, The projection onto the center of operators in a Banach lattice, Math. Z. 199 (1988), no. 1, 115-117. MR 954756 (89f:47058)
9.: A.C. Zaanen, Riesz spaces II, North Holland, Amsterdam, 1983. MR 704021 (86b:46001)
10.: X. D. Zhang, On spectral properties of positive operators, Indag. Math. (N.S.) 4 (1993), no. 1, 111-127. MR 1213328 (94b:47047)
11.: X. D. Zhang, Some aspects of the spectral theory of positive operators, Positive operators and semigroups on Banach lattices (Curaçao, 1990). Acta Appl. Math. 27 (1992), no. 1-2, 135-142. MR 1184885 (93j:47056)

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B65, 47A10

Retrieve articles in all Journals with MSC (2000): 47B65, 47A10

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.

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|