Positive elements of left amenable Lau algebras
Mohammadzadeh, B. ; Nasr-Isfahani, R.
Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, p. 319-324 / Harvested from Project Euclid
In the present paper, we deal with a large class of Banach algebras known as Lau algebras. It is well-known that if ${\frak A}$ is a left amenable Lau algebra, then any $f\in {\frak A}$ such that $|fg|=|f|g$ for all $g\in {\frak A}$ with $g\geq 0$ is a scalar multiple of a positive element in ${\frak A}$. We show that this result remains valid for the group algebra $\ell^1(G)$ of any, not necessarily amenable, discrete group $G$. We also give an example which shows that the result is, in general, not true without the hypothesis of left amenability of ${\frak A}$. This resolves negatively an open problem raised by F. Ghahramani and A. T. Lau.
Publié le : 2006-06-14
Classification:  Absolute value,  Lau algebra,  left amenability,  positive element,  46H05,  43A07,  43A20
@article{1148059466,
     author = {Mohammadzadeh, B. and Nasr-Isfahani, R.},
     title = {Positive elements of left amenable Lau algebras},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {12},
     number = {5},
     year = {2006},
     pages = { 319-324},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148059466}
}
Mohammadzadeh, B.; Nasr-Isfahani, R. Positive elements of left amenable Lau algebras. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp.  319-324. http://gdmltest.u-ga.fr/item/1148059466/