Forms of Isometries Between Function Spaces

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2015-12-01
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Roberts, Kathleen
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Mathematics
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Honors Projects and Posters
University Honors Program

The Honors project is potentially the most valuable component of an Honors education. Typically Honors students choose to do their projects in their area of study, but some will pick a topic of interest unrelated to their major.

The Honors Program requires that the project be presented at a poster presentation event. Poster presentations are held each semester. Most students present during their senior year, but may do so earlier if their honors project has been completed.

This site presents project descriptions and selected posters for Honors projects completed since the Fall 2015 semester.

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Abstract

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.

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