Journal ArticleDOI
Metrizations of orthogonality and characterizations of inner product spaces
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In this paper, the authors present metrized versions of some of these properties and relationships and obtain new characterizations of real inner product spaces among complete, convex, externally convex metric spaces.Abstract:
Characterizations of real inner product spaces among normed linear spaces have been obtained by exploring properties of and relationships between various orthogonality relations which can be defined in such spaces. In the present paper the authors present metrized versions of some of these properties and relationships and obtain new characterizations of real inner product spaces among complete, convex, externally convex metric spaces.read more
Citations
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Journal ArticleDOI
Orthogonality connected with integral means and characterizations of inner product spaces
TL;DR: In this article, the authors introduced notions of orthogonality in terms of the 2−HH norm, and their properties are studied, including characterizations of inner product spaces and strictly convex spaces.
Journal ArticleDOI
Weak homogeneity of metric pythagorean orthogonality
TL;DR: In this paper, the linearity requirement is replaced by the requirement of convexity of the set of points which are metrically pythagorean orthogonal to a given segment at a given point.
Journal ArticleDOI
Intrinsic four-point properties
TL;DR: In this article, the authors provide characterizations of euclidean or hyperbolic spaces based on intrinsic four point properties which are related to known four point embedding properties.
Journal ArticleDOI
Weak additivity of metric pythagorean orthogonality
TL;DR: In this paper, it is shown that a weakened version of this additivity of metric pythagorean orthogonality characterizes real inner product spaces among complete, convex, externally convex metric spaces, providing a generalization of the earlier characterization.
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Book ChapterDOI
Normed Linear Spaces
TL;DR: A(D) as discussed by the authors is a function space with norm ∥ ∥ [Definition I, 3, 1] which defines the topology of major interest in the space; a neighborhood basis of a point x is the family of sets {y: ∥ x - y ∥ ≦ e}.
Journal ArticleDOI
Normed Linear Spaces. By M. M. Day. Pp. 139. DM 28. 1958. (Springer, Berlin)
BookDOI
Characterizations of inner product spaces
TL;DR: In this paper, the Garkavi-Klee condition was combined with the Hahn-Banach Theorem for 3D-approximation and optimal sets, and the symmetry of Orthogonality with smoothness.