Metrizations of orthogonality and characterizations of inner product spaces

DOI10.1007/BF01222138zbMath0719.46012OpenAlexW2075882124MaRDI QIDQ2640098

Raymond W. Freese, Edward Z. Andalafte

Publication date: 1990

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01222138

zbMATH Keywords

Birkhoff orthogonalityPythagorean orthogonalitycharacterizations of real inner product spacescomplete, convex, externally convex metric spaceMetric pythagorean orthogonality

Mathematics Subject Classification ID

Complete metric spaces (54E50) Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Characterizations of Hilbert spaces (46C15) Quadratic and bilinear forms, inner products (15A63)

Related Items (8)

Orthogonality Types in Normed Linear Spaces ⋮ Weak additivity of metric Pythagorean orthogonality ⋮ Weak homogeneity of metric pythagorean orthogonality ⋮ Orthogonality connected with integral means and characterizations of inner product spaces ⋮ Intrinsic four-point properties ⋮ Pythagorean Euclidean four point properties ⋮ Strong additivity of metric isosceles orthogonality ⋮ Altitude properties and characterizations of inner product spaces

Cites Work

• An equilateral four point property which characterizes generalized Euclidean spaces
• Orthogonality in linear metric spaces
• Orthogonality in normed linear spaces
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