Minkowski Space Generalized Orthogonality And Related Nature Of The Study

In the Euclidean space,the feature of generalized orthogonality arenearly perfect. With the Minkowski spaces(Real fnite dimensionalnormed linear space) develop deeply,More and more mathematiciansconcentrate on the research of orthogonality. Extending related prop-erties and conclusions of the generalized orthogonality in Euclideanspace to normed linear spaces has become today's important issues.This article focuses on the uniqueness and the linear operator preserv-ing of Pythagorean orthogonality in real normed linear space.Proof therelevant conclusions, complete the knowledge of generalized orthogo-nality.This article frstly analyzes the development research purpose, sig-nifcance, and the trend of the generalized orthogonality in the con-tent; Secondly we introduced the theroy in Minkowski space,the na-ture of Pythagorean Orthogonality; Finally we proof the uniqueness ofPythagorean Orthogonality in the strictly convex spaces and the na-ture of linear operator of preserving Pythagorean Orthogonality. Andthe content is relatively clear,the structure is also more reasonable.In the paper,we prove two conclusions.First,we give another wayof the uniqueness of Pythagorean Orthogonality in strictly convex s-paces.And the method is more simple and clear. Secondly,we forceson linear operator of the preserving Pythagorean Orthogonality andgive a conclusion: Let X is a normed linear space,T=0is a linearoperator in X.if the Pythagorean Orthogonality in X contains the na-ture of H,and the norm of X is Gateaux diferentiable, T preservesPythagorean Orthogonality, then T is a constant multiple of the i-sometry. The two conclusions consummate the theory of Pythagorean Orthogonality,and it has important theoretical value.