# Multiplicatively spectrum preserving maps of function algebras II

## 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(ƒ*g*)=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*.

## 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

## Additional Details

Thursday, 29 April 2004

4:10 p.m. in Jour 304