Deconstruction of Real-Linear Surjective Isometries Over Complex Vector Spaces
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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
Let V and W be complex inner product spaces; let T be a surjective real-linear isometry from V to W. We show that there exist unique mappings T1 and T2, which are complex-linear and conjugate-linear respectively, such that T = T1 + T2. We use this deconstruction in a new proof of the characterization of the isometries on the complex plane. Furthermore, we present necessary and sufficient conditions under which V is the direct sum of the kernels of T1 and T2.