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Displaying similar documents to “On Riesz homomorphisms in unital f -algebras”

Riesz spaces of order bounded disjointness preserving operators

Fethi Ben Amor (2007)

Commentationes Mathematicae Universitatis Carolinae

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Let L , M be Archimedean Riesz spaces and ℒ b ( L , M ) be the ordered vector space of all order bounded operators from L into M . We define a Lamperti Riesz subspace of ℒ b ( L , M ) to be an ordered vector subspace ℒ of ℒ b ( L , M ) such that the elements of ℒ preserve disjointness and any pair of operators in ℒ has a supremum in ℒ b ( L , M ) that belongs to ℒ . It turns out that the lattice operations in any Lamperti Riesz subspace ℒ of ℒ b ( L , M ) are given pointwise, which leads to a generalization of the classic Radon-Nikod’ym theorem...

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...

A short proof on lifting of projection properties in Riesz spaces

Marek Wójtowicz (1999)

Commentationes Mathematicae Universitatis Carolinae

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Let L be an Archimedean Riesz space with a weak order unit u . A sufficient condition under which Dedekind [ σ -]completeness of the principal ideal A u can be lifted to L is given (Lemma). This yields a concise proof of two theorems of Luxemburg and Zaanen concerning projection properties of C ( X ) -spaces. Similar results are obtained for the Riesz spaces B n ( T ) , n = 1 , 2 , ⋯ , of all functions of the n th Baire class on a metric space T .