The Peripheral Spectrum and Function Algebra Isomorphisms

Document Type

Presentation Abstract

Presentation Date

5-1-2008

Abstract

There is a long history of studying linear maps between Banach algebras that preserve some non-algebraic structure, such as invertibility or the norms of elements, and determining whether this necessarily implies the map must also have further algebraic structure, such as being multiplicative or a weighted composition operator. In recent years, researchers have begun to ask similar questions about maps that are not assumed to be linear. Here we will present results demonstrating that maps between uniform algebras or Lipschitz algebras that satisfy certain preservation properties with respect to subsets of the spectrum must be isometric algebra isormorphisms or weighted composition operators, and this holds regardless of the fact that we do not assume the linearity of the maps.

Additional Details

Thursday, 1 May 2008
4:10 p.m. in 103
3:30 p.m. Refreshments in Math Lounge 109

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