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Extension and inversion of extended orthomorphisms on Riesz spaces
- Part of
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- Journal:
- Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics / Volume 37 / Issue 2 / October 1984
- Published online by Cambridge University Press:
- 09 April 2009, pp. 223-242
- Print publication:
- October 1984
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- Article
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Let E be an Archimedean Riesz space and let Orth∞(E) be the f-algebra consisting of all extended orthomorphisms on E, that is, of all order bounded linear operators T:D→E, with D an order dense ideal in E, such that T(B∩D) ⊆ B for every band B in E. We give conditions on E and on a Riesz subspace F of E insuring that every T ∈ Orth∞(F) can be extended to some
∈ Orth∞(E), and we also consider the problem of inversing an extended orthomorphism on its support. The same problems are also studied in the case of σ-orthomorphisms, that is, extended orthomorphisms with a super order dense domain. Furthermore, some applications are given.
∈ Orth