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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Subordinated discrete semigroups of operators


Author: Nick Dungey
Journal: Trans. Amer. Math. Soc. 363 (2011), 1721-1741
MSC (2000): Primary 47A30; Secondary 60G50, 47A60, 47D06
Published electronically: November 15, 2010
MathSciNet review: 2746662
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Abstract: Given a power-bounded linear operator $ T$ in a Banach space and a probability $ F$ on the non-negative integers, one can form a `subordinated' operator $ S = \sum_{k\geq 0} F(k) T^k$. We obtain asymptotic properties of the subordinated discrete semigroup $ (S^n\colon n=1,2, \ldots)$ under certain conditions on $ F$. In particular, we study probabilities $ F$ with the property that $ S$ satisfies the Ritt resolvent condition whenever $ T$ is power-bounded. Examples and counterexamples of this property are discussed. The hypothesis of power-boundedness of $ T$ can sometimes be replaced by the weaker Kreiss resolvent condition.


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Additional Information

Nick Dungey
Affiliation: Department of Mathematics, Macquarie University, NSW 2109, Australia

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05094-9
PII: S 0002-9947(2010)05094-9
Keywords: Power-bounded operator, Ritt operator, discrete semigroup, analytic semigroup, subordinated semigroup
Received by editor(s): January 27, 2008
Published electronically: November 15, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.