Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415059 | Journal of Functional Analysis | 2016 | 15 Pages |
Abstract
Let B be a semiprime commutative unital Banach algebra with connected character space ΦB. For each xâΦB, let ÏB(x) be the collection of all closed primary ideals contained in the maximal ideal M(x)=xâ1(0). The purpose of this paper is to illustrate how knowledge of the collection ÏB(x) at each xâΦB can be used in describing the outer spectrum of a quasi-compact unital endomorphism of B. Among other things, our results lead to the observation that when B is strongly regular, every Riesz endomorphism of B is quasi-nilpotent on an invariant maximal ideal. Some of the implications of our work for various other types of function algebra are explored at the end of the paper.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
D. Moore,