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On Some Skew Constants in Banach Spaces

Qi Liu|Yongjin Li|Zhijian Yang|Yuankang Fu
경북대학교 자연과학대학 수학과|2023.06|Kyungpook Mathematical Journal|제63권 제2호|pp. 199-223|DOI 10.5666/KMJ.2023.63.2.199

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키워드

normal structuregeometric constantuniform non-squareness
주제분류수학

초록

We introduce the constants E[t, X], CNJ[X] and J[t, X] to describe the asym metry 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 proper ties 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

Abstract

We introduce the constants E[t, X], CNJ[X] and J[t, X] to describe the asym metry 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 proper ties 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

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