Domination properties in ordered Banach algebras

• Autorzy: H. du T. Mouton , S. Mouton
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 47B65: Positive operators and order-bounded operators
• 06F25: Ordered rings, algebras, modules
• 46H05: General theory of topological algebras
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2002
• Tom: 149
• Numer: 1
• Strony: 63-73

Daty

wydano

2002

Twórcy

autor

H. du T. Mouton

• Department of Electrical and Electronic Engineering, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa

autor

S. Mouton

• Department of Mathematics, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa

Identyfikatory

DOI

10.4064/sm149-1-4