#### Event Title

#### Date

12-2015 12:00 AM

#### Major

Mathematics

#### Department

Mathematics

#### College

College of Liberal Arts and Sciences

#### Project Advisor

Kristopher Lee

#### Project Advisor's Department

Mathematics

#### Description

The classic Banach-Stone Theorem establishes a form for surjective, complex-linear isometries (distance preserving functions) between function spaces. Mathematician Takeshi Miura from Niigata University questioned what could be said about surjective, real-linear isometries after finding a counter-example that demonstrated the shortcomings of the Banach-Stone Theorem to classify such functions. Through a careful examination of the Banach-Stone we found why the theorem does not hold in general and proved a theorem that gives a form for real-linear isometries between function spaces.

#### File Format

application/pdf

#### Included in

Forms of Isometries Between Function Spaces

The classic Banach-Stone Theorem establishes a form for surjective, complex-linear isometries (distance preserving functions) between function spaces. Mathematician Takeshi Miura from Niigata University questioned what could be said about surjective, real-linear isometries after finding a counter-example that demonstrated the shortcomings of the Banach-Stone Theorem to classify such functions. Through a careful examination of the Banach-Stone we found why the theorem does not hold in general and proved a theorem that gives a form for real-linear isometries between function spaces.