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Journal of Shanghai University（Natural Science Edition）

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Isotropic Constant of Bpn and Its Asymptotic Properties

XUE Lian1,2, CHEN Qiao-yun1,3, HE Bin-wu1   

  1. 1.College of Sciences, Shanghai University, Shanghai 200444, China;
    2.College of Sciences, Nantong University, Nantong 226001, Jiangsu, China;
    3.Department of Mathematics, Lishui University, Lishui 323000, Zhejiang, China
  • Received:2007-01-17 Revised:1900-01-01 Online:2008-06-30 Published:2008-06-30
  • Contact: HE Bin-wu

Abstract: Let Bpn={x∈Rn | ‖x‖p≤1} be a unit ball of n-dimension normed space lpn. It is shown that Bpn is isotropic convex body if 1≤p≤∞, and the isotropic constant formula of Bpn is given.Moreover, asymptotic properties of isotropic constant of Bpn is obtained as n→∞ and p→∞

Key words: asymptotic properties, isotropic constant, normed space, unit ball

CLC Number: