Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Some Skew Constants in Banach Spaces

  • Yuankang Fu (Department of Mathematics, Sun Yat-sen University) ;
  • Zhijian Yang (Department of Mathematics, Sun Yat-sen University) ;
  • Yongjin Li (Department of Mathematics, Sun Yat-sen University) ;
  • Qi Liu (School of Mathematics and Physics, Anqing Normal University)
  • Received : 2022.05.02
  • Accepted : 2023.03.14
  • Published : 2023.06.30
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Abstract

We introduce the constants E[t, X], CNJ[X] and J[t, X] to describe the asymmetry of the norm. They can be seen as the skew version of the Gao's parameter, von Neumann-Jordan constant and Milman's moduli, respectively. We establish basic properties of these constants, relating them other well known constants, and use these properties to calculate the constants for specific spaces. We then use these constants to study Hilbert spaces, uniformly non-square spaces and their normal structures. With the Banach-Mazur distance, we use them to study isomorphic Banach spaces.

Keywords

Acknowledgement

The authors gratefully thank the referees for their helpful comments.

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