The automorphism group and the non-self-duality of p-cones

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:471

Article

Ito, Masaru¹  Lourenco, Bruno F.² 

[1] Nihon Univ, Coll Sci & Technol, Dept Math, Chiyoda Ku, 1-8-14 Kanda Surugadai, Tokyo 1018308, Japan

[2] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1138656, Japan

关键词: p-cone;    Automorphisin group;    Self-duality;   

DOI  :  10.1016/j.jmaa.2018.10.081

来源: Elsevier

【 摘 要 】

In this paper, we determine the automorphism group of the p-cones (p not equal 2) in dimension greater than two. In particular, we show that the automorphism group of those p-cones are the positive scalar multiples of the generalized permutation matrices that fix the main axis of the cone. Next, we take a look at a problem related to the duality theory of the p-cones. Under the Euclidean inner product it is well-known that a p-cone is self-dual only when p = 2. However, it was not known whether it is possible to construct an inner product depending on p which makes the p-cone self-dual. Our results show that no matter which inner product is considered, a p-cone will never become self-dual unless p = 2 or the dimension is less than three. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free