Advances in Operator Theory

wUR modulus and normal structure in Banach spaces

Ji Gao

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‎Let $X$ be a Banach space‎. ‎In this paper‎, ‎we study the properties of wUR modulus of $X$‎, ‎$\delta_X(\varepsilon‎, ‎f),$ where $0 \le \varepsilon \le 2$ and $f \in S(X^*),$ and the relationship between the values of wUR modulus and reflexivity‎, ‎uniform nonsquareness and normal structure‎, ‎respectively‎. ‎Among other results‎, ‎we proved that if $ \delta_X(1‎, ‎f)> 0$‎, ‎for any $f\in S(X^*)$‎, ‎then $X$ has weak normal structure‎.

Article information

Adv. Oper. Theory, Volume 3, Number 3 (2018), 639-646.

Received: 14 January 2018
Accepted: 27 February 2018
First available in Project Euclid: 4 April 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46B20: Geometry and structure of normed linear spaces
Secondary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]

uniform convexity‎ ‎normal structure ‎wUR


Gao, Ji. wUR modulus and normal structure in Banach spaces. Adv. Oper. Theory 3 (2018), no. 3, 639--646. doi:10.15352/aot.1801-1295.

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