Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and ge...Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the <em>l<sub>p</sub></em> space.展开更多
In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make us...In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.展开更多
文摘Firstly, in the general normed linear space, the concepts of generalized isosceles orthogonal group, generalized Birkhoff orthogonal group, generalized Roberts orthogonal group, strong Birkhoff orthogonal group and generalized orthogonal basis are introduced. Secondly, the conclusion that any two nonzero generalized orthogonal groups must be linearly independent group is proven. And the existence of nonzero generalized orthogonal group and its linear correlation are discussed preliminarily, as well as some related properties of nonempty generalized orthogonal group in specific normed linear space namely the <em>l<sub>p</sub></em> space.
文摘In this paper,we study Tingley＇s problem on symmetric absolute normalized norms on R^2.We construct new methods for Tingley＇s problem on two-dimensional spaces by using isosceles orthogonality,which does not make use of the notion of natural extension.Furthermore,using our methods,several sufficient conditions for Tingley＇s problem on symmetric absolute normalized norms on R2 are given.As applications,we present various new examples including the two-dimensional Lorentz sequence space d^（2）（ω,q） and its dual d^（2）（ω,q）＊by simple arguments.
