A Coefficient Related to Some Geometric Properties of a Banach Space

Zuo, Zhanfei; Cui, Yunan

doi:10.1155/2009/934321

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Introduction4

The Generalized Von Neumann-jordan Constant and Uniform1

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Cited by 5 publications

(8 citation statements)

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“…It has been shown that these constants are very useful in geometric theory of Banach spaces, which enable us to classify several important concepts of Banach spaces such as uniformly non-squareness and uniform normal structure [3][4][5][6][7][8]. On the other hand, calculation of the constant for some concrete spaces is also of some interest [5,6,9].…”

Section: Introductionmentioning

confidence: 99%

The Ptolemy constant of absolute normalized norms on ℝ2

Zuo

2012

J Inequal Appl

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Section: Introductionmentioning

confidence: 99%

The Ptolemy constant of absolute normalized norms on ℝ2

Zuo

2012

J Inequal Appl

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“…Proof. Since X is uniformly non-square, so X is super-reflexive(see [13]), and consequently it is enough to show that X has normal structure. Suppose that X lacks normal structure.…”

Section: The Generalized Von Neumann-jordan Constant and Uniformmentioning

confidence: 99%

The generalized von Neumann--Jordan constant and normal structure in Banach spaces

Xi¹,

Cui²,

Zhang³

2015

Ann. Funct. Anal.

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Recently, a new geometric constant called generalized von Neumann-Jordan constant was introduced. In this paper, the relationships between above constant and generalized García-Falset coefficient are given. In terms of this constant, the lower bounds for the weakly convergent sequence coefficient of a Banach space X are also shown. Moreover, some sufficient conditions which imply normal structure and uniform normal structure are presented.

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“…In [6], the modulus of Zuo-Cui was introduced in Banach spaces. The author proved many results with this special type of modulus.…”

Section: Introductionmentioning

confidence: 99%