On algebra homomorphisms in complex almost f -algebras

Abdelmajid Triki

Commentationes Mathematicae Universitatis Carolinae (2002)

  • Volume: 43, Issue: 1, page 23-31
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Triki, Abdelmajid. "On algebra homomorphisms in complex almost $f$-algebras." Commentationes Mathematicae Universitatis Carolinae 43.1 (2002): 23-31. <http://eudml.org/doc/248967>.

@article{Triki2002,
abstract = {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.},
author = {Triki, Abdelmajid},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {vector lattice; order bounded operator; lattice ordered algebra; $f$-algebra; almost $f$-algebra; vector lattice; order-bounded operator; lattice-ordered algebra; -algebra; almost -algebra},
language = {eng},
number = {1},
pages = {23-31},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On algebra homomorphisms in complex almost $f$-algebras},
url = {http://eudml.org/doc/248967},
volume = {43},
year = {2002},
}

TY - JOUR
AU - Triki, Abdelmajid
TI - On algebra homomorphisms in complex almost $f$-algebras
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2002
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 43
IS - 1
SP - 23
EP - 31
AB - 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.
LA - eng
KW - vector lattice; order bounded operator; lattice ordered algebra; $f$-algebra; almost $f$-algebra; vector lattice; order-bounded operator; lattice-ordered algebra; -algebra; almost -algebra
UR - http://eudml.org/doc/248967
ER -

References

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  1. Beukers F., Huijsmans C.B., Pagter B. de, Unital embedding and complexification of f -algebras, Math. Z. 183 131-144 (1983). (1983) MR0701362
  2. Huijsmans C.B., Pagter, B. de, Averaging operators and positive contractive projections, J. Math. Anal. Appl. 113 163-184 (1986). (1986) Zbl0604.47024MR0826666
  3. Huijsmans C.B., Pagter B. de, Subalgebras and Riesz subspaces of an f -algebra, Proc. London Math. Soc. (3) 48 161-174 (1984). (1984) Zbl0534.46010MR0721777
  4. Luxemburg W.A.J., Zaanen A.C., Riesz Spaces I, North Holland, Amsterdam, 1971. 
  5. Nagasawa M., Isomorphisms between commutative Banach algebras with an application to rings of analytic functions, Kodai Math. Semin. Rep. 11 182-188 (1959). (1959) Zbl0166.40002MR0121645
  6. Quinn J., Intermediate Riesz spaces, Pacific J. Math. 56 (1975), 225-263. (1975) Zbl0315.06009MR0380355
  7. Schaefer H.H., Banach Lattices and Positive Operators, Springer, Berlin, 1974. Zbl0296.47023MR0423039
  8. Scheffold E., FF-Banachverband algebren, Math. Z. 177 193-205 (1981). (1981) MR0612873
  9. Zaanen A.C, Riesz Spaces II, North-Holland, Amsterdam, 1983. Zbl0519.46001MR0704021

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