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.