The James constant for the l 3 − l 1 space

2016 ◽  
Vol 32 (9) ◽  
pp. 1075-1079 ◽  
Author(s):  
Chang Sen Yang ◽  
Hai Ying Li
Keyword(s):  
James Constant

scholarly journals Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1285
Author(s):  
Asif Ahmad ◽  
Yuankang Fu ◽  
Yongjin Li
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Geometric Properties ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Constants

In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,▵), L2(X,▵) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,▵), L2(X,▵), and calculate the bounds of L1(X,▵) and L2(X,▵) as well as the values of L1(X,▵) and L2(X,▵) for two Banach spaces.

scholarly journals On the calculation of the James constant of Lorentz sequence spaces

2008 ◽  
Vol 343 (1) ◽  
pp. 310-314 ◽  
Author(s):  
Ken-Ichi Mitani ◽  
Kichi-Suke Saito ◽  
Tomonari Suzuki
Keyword(s):  
Sequence Spaces ◽  
James Constant

scholarly journals On a generalized James constant

2003 ◽  
Vol 285 (2) ◽  
pp. 419-435 ◽  
Author(s):  
S. Dhompongsa ◽  
A. Kaewkhao ◽  
S. Tasena
Keyword(s):  
James Constant

scholarly journals James constant for interpolation spaces

2011 ◽  
Vol 382 (1) ◽  
pp. 127-131
Author(s):  
Anna Betiuk-Pilarska ◽  
Supaluk Phothi ◽  
Stanisław Prus
Keyword(s):  
Interpolation Spaces ◽  
James Constant

scholarly journals On the class of Banach spaces with James constant √2, III

2017 ◽  
pp. 865-887
Author(s):  
Naoto Komuro ◽  
Kichi-Suke Saito ◽  
Ryotaro Tanaka
Keyword(s):  
Banach Spaces ◽  
James Constant

scholarly journals On the class of Banach spaces with James constant √2, III

2017 ◽  
pp. 865-887
Author(s):  
Naoto Komuro ◽  
Kichi-Suke Saito ◽  
Ryotaro Tanaka
Keyword(s):  
Banach Spaces ◽  
James Constant

More moduli and coefficients

2018 ◽  
pp. 85-101
Author(s):  
Kazimierz Goebel ◽  
Stanisław Prus
Keyword(s):  
Uniform Convexity ◽  
General Construction ◽  
Two Dimensional ◽  
James Constant ◽  
Uniform Smoothness

The general construction of multi-dimensional Milman’s moduli is described. Two-dimensional moduli are related to uniform convexity and uniform smoothness. The James constant measuring nonsquareness of the ball is discussed. A universal modulus, called also the modulus of squareness, and related both to convexity and smoothness is studied.

On the Class of Banach Spaces with James Constant $${\sqrt{2}}$$ 2 : Part II

2016 ◽  
Vol 13 (6) ◽  
pp. 4039-4061 ◽  
Author(s):  
Naoto Komuro ◽  
Kichi-Suke Saito ◽  
Ryotaro Tanaka
Keyword(s):  
Banach Spaces ◽  
James Constant
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