The Additive Operator Preserving Birkhoff Orthogonal

Sanxing Guo

Science of College, Tianjin University of Technology, Tianjin, China.

DOI: 10.4236/jamp.2019.73036                

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.

Keywords

Birkhoff Orthogonal, Additive Operator, Smooth Point

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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