Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y i...Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq（x,y）=π/2. Some other properties of this angle are also discussed.展开更多
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 introduce the definition of generalized Day-James space on Rn （n 〉 2） and give a characterization of it, which extend some known results. In addition, we provide a sufficient and necessary conditi...In this paper, we introduce the definition of generalized Day-James space on Rn （n 〉 2） and give a characterization of it, which extend some known results. In addition, we provide a sufficient and necessary condition for Day-James space, which reappeared Day＇s construction for any two-dimensional normed space to make Birkhoff orthogonality symmetry.展开更多
文摘Let X be a Minkowski plane, i.e., a real two dimensional normed linear space. We use projections to give a definition of the angle Aq（x, y） between two vectors x and y in X, such that x is Birkhoff orthogonal to y if and only if Aq（x,y）=π/2. Some other properties of this angle are also discussed.
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.
基金Supported by National Natural Science Foundation of China(Grant Nos.61403290,61373174 and 11401451)
文摘In this paper, we introduce the definition of generalized Day-James space on Rn （n 〉 2） and give a characterization of it, which extend some known results. In addition, we provide a sufficient and necessary condition for Day-James space, which reappeared Day＇s construction for any two-dimensional normed space to make Birkhoff orthogonality symmetry.
