Extension and inversion of extended orthomorphisms on Riesz spaces
1984 ◽
Vol 37
(2)
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pp. 223-242
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Keyword(s):
AbstractLet 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.
Keyword(s):
Keyword(s):
2008 ◽
Vol 108
(1)
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pp. 81-87
2008 ◽
Vol 2008
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pp. 1-9
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Keyword(s):
2020 ◽
Vol 0
(0)
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