Domination properties in ordered Banach algebras

H. du T. Mouton, and S. Mouton. "Domination properties in ordered Banach algebras." Studia Mathematica 149.1 (2002): 63-73. <http://eudml.org/doc/284858>.

@article{H2002,
abstract = {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.},
author = {H. du T. Mouton, S. Mouton},
journal = {Studia Mathematica},
keywords = {ordered Banach algebra; positive element; subharmonic analysis},
language = {eng},
number = {1},
pages = {63-73},
title = {Domination properties in ordered Banach algebras},
url = {http://eudml.org/doc/284858},
volume = {149},
year = {2002},
}

TY - JOUR
AU - H. du T. Mouton
AU - S. Mouton
TI - Domination properties in ordered Banach algebras
JO - Studia Mathematica
PY - 2002
VL - 149
IS - 1
SP - 63
EP - 73
AB - 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.
LA - eng
KW - ordered Banach algebra; positive element; subharmonic analysis
UR - http://eudml.org/doc/284858
ER -