Advances in Operator Theory

wUR modulus and normal structure in Banach spaces

Ji Gao

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Abstract

‎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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aot/1522807281

Digital Object Identifier
doi:10.15352/aot.1801-1295

Mathematical Reviews number (MathSciNet)
MR3795105

Zentralblatt MATH identifier
06902457

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

Keywords
uniform convexity‎ ‎normal structure ‎wUR

Citation

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. https://projecteuclid.org/euclid.aot/1522807281


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