We recall from [9] the definition and properties of an algebra cone C of a real or complex Banach algebra A. It can be shown that C induces on A an ordering which is compatible with the algebraic structure of A. The Banach algebra A is then called an ordered Banach algebra. An important property that the algebra cone C may have is that of normality. If C is normal, then the order structure and the topology of A are reconciled in a certain way. Ordered Banach algebras have interesting spectral properties. If A is an ordered Banach algebra with a normal algebra cone C, then an important problem is that of providing conditions under which certain spectral properties of a positive element b will be inherited by positive elements dominated by b. We are particularly interested in the property of b being an element of the radical of A. Some interesting answers can be obtained by the use of subharmonic analysis and Cartan's theorem.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-1-4,
author = {H. du T. Mouton and S. Mouton},
title = {Domination properties in ordered Banach algebras},
journal = {Studia Mathematica},
volume = {151},
year = {2002},
pages = {63-73},
zbl = {1001.46030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-1-4}
}
H. du T. Mouton; S. Mouton. Domination properties in ordered Banach algebras. Studia Mathematica, Tome 151 (2002) pp. 63-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm149-1-4/