Original Articles

THE PERIPHERAL SPECTRUM IN BANACH LATTICE ALGEBRAS

Published in: Quaestiones Mathematicae
Volume 12 , issue 2 , 1989 , pages: 175–185

DOI: 10.1080/16073606.1989.9632174

Author(s): Lucas Venter Department of Mathematics and Applied Mathematics, Republic of South Africa , JacobusJ. Grobler Department of Mathematics and Applied Mathematics, Republic of South Africa , Peter van Eldik Department of Mathematics and Applied Mathematics, Republic of South Africa

Keywords: 46A40 , 47B55

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Abstract

We describe the peripheral spectrum of positive elements of a complex Banach lattice algebra E by exploiting the order structure of the space, the properties of the set M of non-trivial multiplicative linear functionals on E, and of appropriate subsets of M. The theory of f-algebras plays a major rôle in our discussion. All proofs are elementary in the sense that they contain no representation theory.

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