数学物理学报(英文版)

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CHARACTERIZATION OF SOLID CONES

丘京辉   

  1. 苏州大学数学系, 苏州 215006
  • 收稿日期:2005-08-12 修回日期:2006-06-15 出版日期:2008-04-20 发布日期:2008-04-20
  • 通讯作者: 丘京辉
  • 基金资助:

    Supported by the National Natural Science Foundation of China (10571035)

CHARACTERIZATION OF SOLID CONES

Qiu Jinghui   

  1. Department of Mathematics, Suzhou University, Suzhou 215006, China
  • Received:2005-08-12 Revised:2006-06-15 Online:2008-04-20 Published:2008-04-20
  • Contact: Qiu Jinghui

摘要:

The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the
framework of Banach spaces. In particular, the author gives a dual
relationship between solid cones and generalized sharp cones. The
related known results are improved and extended.

关键词: Convex cones, solid cones, bases of cones, angle property,
locally convex spaces

Abstract:

The author gives a dual characterization of solid cones in locally convex spaces. From this the author obtains some criteria for judging convex cones to be solid in various kinds of locally convex spaces. Using a general expression of the interior of a solid cone, the author obtains a number of necessary and sufficient conditions for convex cones to be solid in the
framework of Banach spaces. In particular, the author gives a dual
relationship between solid cones and generalized sharp cones. The
related known results are improved and extended.

Key words: Convex cones, solid cones, bases of cones, angle property,
locally convex spaces

中图分类号: 

  • 46A20