Disjointness Preserving Operators on Complex Riesz Spaces |
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Authors: | Grobler J J Huijsmans C B |
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Abstract: | It is proven that ifE
and F
are complex Riesz spaces and ifT is an order bounded disjointness preserving operator fromE
intoF
, then
This fundamental result of M. Meyer is obtained by elementary means using as the main tool the functional calculus derived from the Freudenthal spectral theorem. It is also shown that ifT is an order bounded disjointness preserving operator, a formula of the form
holds. It implies a polar decomposition of an order bounded disjointness preserving operator as the product of a Riesz homomorphism and an orthomorphism. Results of P. Meyer-Nieberg in this regard are generalized. |
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Keywords: | disjointness preserving operator orthomorphism Riesz homomorphism |
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