Complex structures on real vector lattices (Q289532)
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scientific article; zbMATH DE number 6587130
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complex structures on real vector lattices |
scientific article; zbMATH DE number 6587130 |
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Complex structures on real vector lattices (English)
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30 May 2016
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The author studies conditions for a real vector lattice to admit a band preserving complex structure. It turns out that there is no order bounded band preserving complex structure on an Archimedean vector lattice. The main result states that each real non-locally-one-dimensional universally complete vector lattice admits some band preserving but not order bounded complex structure and such a structure is isomorphic to the complexification of some real vector lattice.
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complex structure
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universally complete vector lattice
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band preserving operator
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locally one-dimensional vector lattice
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