The Additive Operator Preserving Birkhoff Orthogonal ()
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.
Share and Cite:
Guo, S. (2019) The Additive Operator Preserving Birkhoff Orthogonal.
Journal of Applied Mathematics and Physics,
7, 505-512. doi:
10.4236/jamp.2019.73036.
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