Displaying similar documents to “A note on Riesz elements in C * -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...