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

Analysis Commons

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Dec 1st, 12:00 AM

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.