About this Mathematics article
Multiplicative Representation of Disjointness Preserving Operators by Yuri A. Abramovich is a Mathematics article available to read on EtoBox.
Let Xand Y be vector lattices and let T : X+ Y be a disjointness preserving linear operator, i.e., ITx~jAlT.x,l=O if lxriAlx2J =O; xr,xzoX. Necessary and sufficient conditions are obtained under which T can be written as a multiplication, i.e., where r is a continuous mapping from a topological space on which Ycan be represented as a vector lattice of extended real valued continuous functions into a topological space on which X can be similarly represented. If X and Y are normed lattices and T is continuous, these conditions are satisfied and hence T can be represented as such a multiplication. With the author's permission, several remarks made by C.B. Huijsmans and B. de Pagter are incorporated in the text.
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- Author
- Yuri A. Abramovich
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 1385-7258)
- Published
- 1983
- Language
- EN
- Field
- Mathematics (Physical Sciences)