Domination problem for narrow orthogonally additive operators |
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Authors: | Marat Pliev |
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Institution: | 1.Southern Mathematical Institute of the Russian Academy of Sciences,Vladikavkaz,Russia |
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Abstract: | The “Up-and-down” theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result in operator theory. We prove an analog of this theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result is used to prove a theorem of domination for order narrow positive abstract Uryson operators from a vector lattice E to a Banach lattice F with an order continuous norm. |
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