The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner produ...The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.展开更多
基金supported by the National Natural Science Foundation of China(12071444,12201581)the Fundamental Research Program of Shanxi Province of China(202103021223191).
文摘The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.
