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 → A a Riesz homomorphism such that T 2 ( f ) = T ( f T ( e ) ) for all f ∈ A . Then every Riesz homomorphism extension T ˜ of T from the Dedekind completion A δ of A into itself satisfies T ˜ 2 ( f ) = T ˜ ( f T ( e ) ) for all f ∈ 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 < ∞.

On vectorial inner product spaces

João de Deus Marques (2000)

Czechoslovak Mathematical Journal

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Let E be a real linear space. A vectorial inner product is a mapping from E × E into a real ordered vector space Y with the properties of a usual inner product. Here we consider Y to be a ℬ -regular Yosida space, that is a Dedekind complete Yosida space such that ⋂ J ∈ ℬ J = { 0 } , where ℬ is the set of all hypermaximal bands in Y . In Theorem 2.1.1 we assert that any ℬ -regular Yosida space is Riesz isomorphic to the space B ( A ) of all bounded real-valued mappings on a certain set A . Next we prove Bessel Inequality...

Remark on the inequality of F. Riesz

W. Łenski (2005)

Banach Center Publications

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We prove F. Riesz’ inequality assuming the boundedness of the norm of the first arithmetic mean of the functions | φ ₙ | p with p ≥ 2 instead of boundedness of the functions φₙ of an orthonormal system.