| Title:
|
On algebra homomorphisms in complex almost $f$-algebras (English) |
| Author:
|
Triki, Abdelmajid |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
23-31 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Extensions of order bounded linear operators on an Archimedean vector lattice to its relatively uniform completion are considered and are applied to show that the multiplication in an Archimedean lattice ordered algebra can be extended, in a unique way, to its relatively uniform completion. This is applied to show, among other things, that any order bounded algebra homomorphism on a complex Archimedean almost $f$-algebra is a lattice homomorphism. (English) |
| Keyword:
|
vector lattice |
| Keyword:
|
order bounded operator |
| Keyword:
|
lattice ordered algebra |
| Keyword:
|
$f$-algebra |
| Keyword:
|
almost $f$-algebra |
| MSC:
|
06F20 |
| MSC:
|
06F25 |
| MSC:
|
46A40 |
| idZBL:
|
Zbl 1070.06008 |
| idMR:
|
MR1903304 |
| . |
| Date available:
|
2009-01-08T19:19:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119297 |
| . |
| Reference:
|
[1] Beukers F., Huijsmans C.B., Pagter B. de: Unital embedding and complexification of $f$-algebras.Math. Z. 183 131-144 (1983). MR 0701362 |
| Reference:
|
[2] Huijsmans C.B., Pagter, B. de: Averaging operators and positive contractive projections.J. Math. Anal. Appl. 113 163-184 (1986). Zbl 0604.47024, MR 0826666 |
| Reference:
|
[3] Huijsmans C.B., Pagter B. de: Subalgebras and Riesz subspaces of an $f$-algebra.Proc. London Math. Soc. (3) 48 161-174 (1984). Zbl 0534.46010, MR 0721777 |
| Reference:
|
[4] Luxemburg W.A.J., Zaanen A.C.: Riesz Spaces I.North Holland, Amsterdam, 1971. |
| Reference:
|
[5] Nagasawa M.: Isomorphisms between commutative Banach algebras with an application to rings of analytic functions.Kodai Math. Semin. Rep. 11 182-188 (1959). Zbl 0166.40002, MR 0121645 |
| Reference:
|
[6] Quinn J.: Intermediate Riesz spaces.Pacific J. Math. 56 (1975), 225-263. Zbl 0315.06009, MR 0380355 |
| Reference:
|
[7] Schaefer H.H.: Banach Lattices and Positive Operators.Springer, Berlin, 1974. Zbl 0296.47023, MR 0423039 |
| Reference:
|
[8] Scheffold E.: FF-Banachverband algebren.Math. Z. 177 193-205 (1981). MR 0612873 |
| Reference:
|
[9] Zaanen A.C: Riesz Spaces II.North-Holland, Amsterdam, 1983. Zbl 0519.46001, MR 0704021 |
| . |
