| Title:
|
On Riesz homomorphisms in unital $f$-algebras (English) |
| Author:
|
Chil, Elmiloud |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
121-131 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main topic of the first section of this paper is the following theorem: let $A$ be an Archimedean $f$-algebra with unit element $e$, and $T\: A\rightarrow A$ a Riesz homomorphism such that $T^2(f)=T(fT(e))$ for all $f\in A$. Then every Riesz homomorphism extension $\widetilde T$ of $T$ from the Dedekind completion $A^{\delta }$ of $A$ into itself satisfies $\widetilde T^2(f)=\widetilde T(fT(e))$ for all $f\in A^{\delta }$. In the second section this result is applied in several directions.\ As a first application it is applied to show a result about extensions of positive projections to the Dedekind completion. A second application of the above result is a new approach to the Dedekind completion of commutative $d$-algebras. (English) |
| Keyword:
|
vector lattice |
| Keyword:
|
$d$-algebra |
| Keyword:
|
$f$-algebra |
| MSC:
|
06F25 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 1212.06043 |
| idMR:
|
MR2535141 |
| DOI:
|
10.21136/MB.2009.140648 |
| . |
| Date available:
|
2010-07-20T17:53:17Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140648 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
