Real Gel'fand-Mazur division algebras
We show that the complexification (A˜,τ˜) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203211066 |
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| Summary: | We show that the complexification (A˜,τ˜) of a real locally pseudoconvex (locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra (A,τ) is a complex locally pseudoconvex (resp., locally absorbingly pseudoconvex, locally multiplicatively pseudoconvex, and exponentially galbed) algebra and all elements in the complexification (A˜,τ˜) of a commutative real exponentially galbed algebra (A,τ) with bounded elements are bounded if the multiplication in (A,τ) is jointly continuous. We give conditions for a commutative strictly real topological division algebra to be a commutative real Gel'fand-Mazur division algebra. |
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| ISSN: | 0161-1712 1687-0425 |