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Koldobsky, A. (1993) Operators Preserving Orthogonality Are Isometries. Proceedings of the Royal Society of Edinburgh Section A, 123, 835-837.
https://doi.org/10.1017/S0308210500029528

has been cited by the following article:

• TITLE: The Additive Operator Preserving Birkhoff Orthogonal

  AUTHORS: Sanxing Guo

  KEYWORDS: Birkhoff Orthogonal, Additive Operator, Smooth Point

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.3, March 12, 2019

  ABSTRACT: The Birkhoff orthogonal plays an important role in the geometric study of Banach spaces. It has been conrmed that a Birkhoff orthogonality preserving linear operator between two normed linear spaces must necessarily be a scalar multiple of a linear isometry. In this paper, the author gives a new result that a Birkhoff orthogonality preserving additive operator between two-dimensional normed linear spaces is necessarily a scalar multiple of a linear isometry.