LINEAR MAPPINGS PRESEVING ORTHOGONALITY ON BILINEAR SPACES - Sylviani, Sisilia
This dissertation discusses the development of linear mappings that preserve orthogonality in indefinite inner product spaces and bilinear spaces. A linear mapping is said orthogonality preserving if two elements that are orthogonal in the domain result in elements that are orthogonal to each other in the codomain. Many studies have been carried out related to orthogonality preservation properties. One of the most popular studies developed by researchers is the research conducted by Chmieli´nski in 2005. In this research, Chmieli´nski characterizes linear mappings that preserve orthogonality in inner product spaces, which is continuously studied and developed by other researchers. One of them is what W´ojcik did in 2015. This dissertation has succeeded in generalizing those characterizations to indefinite inner product spaces and bilinear spaces. In particular, it has been obtained characterizations of linear mappings that preserve orthogonality in indefinite inner product spaces and bilinear spaces, not only over the real or complex field but also any field including a finite field. The method used to obtain the results in this dissertation is by analyzing the characterization theorem of linear mappings that preserve orthogonality in inner product spaces, then analyze, arrange, and prove equivalent theorem of these facts in the context of indefinite inner product spaces and bilinear spaces.