ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 6, 46 Mouton, Sonja (born Rode), University of Stellenbosch, South Africa Some spectral properties in ordered Banach algebras Let A denote a complex Banach algebra with unit 1. We define an algebra cone C of A and show that C induces on A an ordering “≤“ which is compatible with the algebraic structure of A. A Banach algebra ordered by such an algebra cone is referred to as an ordered Banach algebra (OBA) and the elements of C are called the positive elements. If the order structure and the topology of A is reconciled in a certain way, C is referred to as being normal. We discuss some interesting spectral theoretic results in OBA’s. Reference: H. Raubenheimer and S. Rode, Cones in Banach algebras, Indag. Mathem., N. S. 7(4) (1996), 489 – 502.