Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor

Displaying similar documents to “Riesz spaces of order bounded disjointness preserving operators”

On Riesz homomorphisms in unital $f$ -algebras

Elmiloud Chil (2009)

Mathematica Bohemica

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The main topic of the first section of this paper is the following theorem: let $A$ be an Archimedean $f$ -algebra with unit element $e$ , and $T A \to A$ a Riesz homomorphism such that $T^{2} (f) = T (f T (e))$ for all $f \in A$ . Then every Riesz homomorphism extension $\tilde{T}$ of $T$ from the Dedekind completion $A^{δ}$ of $A$ into itself satisfies ${\tilde{T}}^{2} (f) = \tilde{T} (f T (e))$ for all $f \in A^{δ}$ . In the second section this result is applied in several directions. As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion....

Riesz transforms for the Dunkl Ornstein-Uhlenbeck operator

Adam Nowak, Luz Roncal, Krzysztof Stempak (2010)

Colloquium Mathematicae

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We propose a definition of Riesz transforms associated to the Ornstein-Uhlenbeck operator based on the Dunkl Laplacian. In the case related to the group ℤ ₂ it is proved that the Riesz transform is bounded on the corresponding $L^{p}$ spaces, 1 < p < ∞.