Subordinated discrete semigroups of operators

2008/01/29 by Nick Dungey, Dungey, Nick · 1 citation
Mathematics · #47A30 #60G50 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #math.FA #math.PR #msc:47A30 #msc:60G50

paper · pdf · doi:10.48550/arxiv.0801.4557

28 pages

arxiv created 2008/01/29 · arxiv updated 2009/12/01

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 = ∑_k F(k) T^k. We obtain asymptotic properties of the subordinated discrete semigroup (Sⁿ: n=1,2,...) 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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• Square Functions and Variational Estimates for Ritt Operators on L¹

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