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A Geometric Characterization of Polygonal Radon Planes

Mandal, Kalidas and Sain, Debmalya and Paul, Kallol (2019) A Geometric Characterization of Polygonal Radon Planes. In: JOURNAL OF CONVEX ANALYSIS, 26 (4). pp. 1113-1123.

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Abstract

We study unit circles of polygonal Radon planes from a geometric point of view. In particular, we prove that a two-dimensional real polygonal Banach space X cannot be a Radon plane if the number of vertices of its unit circle is 4n, for some n is an element of N. Also we obtain a complete characterization of polygonal Radon planes in terms of a tractable geometric concept introduced in this article. It follows from our characterization that every regular polygon with 4n+2 vertices, where n is an element of N, is the unit circle of a Radon plane. Furthermore, we describe types of Radon planes for which the unit circles are hexagons, but not regular ones.

Item Type: Journal Article
Additional Information: copyright for this article belongs to HELDERMANN VERLAG
Keywords: Radon plane; Birkhoff-James orthogonality; polygonal Banach space
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 29 Nov 2019 10:25
Last Modified: 29 Nov 2019 10:25
URI: http://eprints.iisc.ac.in/id/eprint/64024

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