Multiplicatively spectrum preserving maps of function algebras II

Authors

Rao Nagisetty

Document Type

Presentation Abstract

Presentation Date

4-29-2004

Abstract

Let cl A be a closed, point-separating sub-algebra of C_û(X)C , where X is a locally compact Hausdorff space. Assume that X is the maximal ideal space of clA . If ƒ∈clA, the set ƒ(X)∪{0} is denoted by σ(ƒ) . After characterizing the points of the Choquet boundary as strong boundary points this equivalence is used to complete the discussion initiated in a previous paper proving the

Main Theorem: If Φ : cl A→cl A is a surjective map with the property that σ(ƒg)=σ(Φ(ƒ)Φ(g)) for every pair of functions ƒ, g∈cl A , then there is an onto homeomorphism Λ: X→X and a signum function g(x) on X such that Φ(ƒ)(Λ(x)) = g(x)ƒ(x) , for all x ∈ X and ƒ∈cl A.

Additional Details

Thursday, 29 April 2004
4:10 p.m. in Jour 304

Recommended Citation

Nagisetty, Rao, "Multiplicatively spectrum preserving maps of function algebras II" (2004). Colloquia of the Department of Mathematical Sciences. 165.
https://scholarworks.umt.edu/mathcolloquia/165