Date

1-4-2017 12:00 AM

Major

Mathematics

Department

Mathematics

College

College of Liberal Arts and Sciences

Project Advisor

Kristopher Lee

Project Advisor's Department

Mathematics

Description

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.

Included in

Mathematics Commons

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Apr 1st, 12:00 AM

Deconstruction of Real-Linear Surjective Isometries Over Complex Vector Spaces

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.