The Additive Operator Preserving Birkhoff Orthogonal - Journal of Applied Mathematics and Physics

JAMP > Vol.7 No.3, March 2019

The Additive Operator Preserving Birkhoff Orthogonal ()

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Download as PDF (Size: 423KB) PP. 505-512

DOI: 10.4236/jamp.2019.73036 594 Downloads 1,096 Views

Author(s)

Sanxing Guo

Affiliation(s)

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

ABSTRACT

The Birkhoff orthogonal plays an important role in the geometric study of Banach spaces. It has been conrmed 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

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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