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A strongly diagonal power of algebraic order bounded disjointness preserving operators. (English) Zbl 1064.47038

Summary: An order bounded disjointness preserving operator \(T\) on an Archimedean vector lattice is algebraic if and only if the restriction of \(T^{n!}\) to the vector sublattice generated by the range of \(T^{m}\) is strongly diagonal, where \(n\) is the degree of the minimal polynomial of \(T\) and \(m\) is its ‘valuation’.

MSC:

47B65 Positive linear operators and order-bounded operators
06F25 Ordered rings, algebras, modules
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References:

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