#### 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

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.