A New Geometric Constant in Banach Spaces Related to the Isosceles Orthogonality

다국어 초록 (Multilingual Abstract)

In this paper, starting with the geometric constants that can characterize Hilbert spaces, combined with the isosceles orthogonality of Banach spaces, the orthogo nal geometric constant ΩX(α) is defined, and some theorems on the geometric properties of Banach spaces are derived. Firstly, this paper reviews the research progress of orthogo nal geometric constants in recent years. Then, this paper explores the basic properties of the new geometric constants and their relationship with conventional geometric constants, and deduces the identity of ΩX (α) and γX(α). Finally, according to the identities, the relationship between these the new orthogonal geometric constant and the geometric prop erties of Banach Spaces (such as uniformly non-squareness, smoothness, convexity, normal structure, etc.) is studied, and some necessary and sufficient conditions are obtained.

참고문헌 (Reference)

1 Y. Takahashi, "Von Neumann-Jordan constant and uniformly non-square Banach spaces" 9 : 155-169, 1998

2 R. C. James, "Uniformly non-square Banach spaces" 80 : 542-550, 1964

3 J. A. Clarkson, "Uniformly convex spaces" 40 : 396-414, 1936

4 M. M. Day, "Uniform convexity in factor and conjugate spaces" 45 : 375-385, 1944

5 J. A. Clarkson, "The von Neumann-Jordan constant for the Lebesgue space" 38 : 114-115, 1937

6 H. Mizuguchi, "The constants to measure the differences between Birkhoffand isosceles orthogonalities" 30 : 2761-2770, 2015

7 Y. Cui, "Some properties concerning Milman’s moduli" 329 : 1260-1272, 2007

8 F. Wang, "Some inequalities concering the James constant in Ba-nach spaces" 353 : 305-310, 2009

9 D. Ji, "Quantitative characterization of the difference between Birkhofforthogonality and isosceles orthogonality" 323 : 1-7, 2006

10 R. C. James, "Orthogonality in normed linear spaces" 12 : 291-302, 1945

11 G. Birkhoff, "Orthogonality in linear metric spaces" 1 : 169-172, 1935

12 J. Lindenstrauss, "On the modulus of smoothness and divergent series in Ba-nach spaces" 10 : 241-252, 1963

13 J. Gao, "On the geometry of spheres in normed linear spaces" 48 : 101-112, 1990

14 B. D. Roberts, "On the geometry of abstract vector spaces" 39 : 42-59, 1934

15 M. Brodskii, "On the center of a convex set" 59 : 837-840, 1948

16 P. Jordan, "On inner products in linear metric spaces" 36 : 719-723, 1935

17 C. Yang, "On estimates of the generalized Jordan-von Neumann constant of Banach spaces" 7 : 1-5, 2006

18 S. Dhompongsa, "On a generalized James constant" 285 : 419-435, 2003

19 L. Qi, "New geometric constants of isosceles orthogonal type"

20 P. L. Papini, "Measurements of differences between orthogonality types" 397 : 285-291, 2013

21 C. Hao, "Homogeneity of isosceles orthogonality and related inequal-ities" 84 : 9-, 2011

22 K. Goebel, "Convexity of balls and fixed point theorems for mapping with non-expansive square" 22 : 269-274, 1970

23 C. Bentez, "Characterization of inner product spaces through rectangle and square inequalities" 29 : 543-546, 1984

24 V. Balestro, "Angles in normed spaces" 91 : 201-236, 2017

25 Y. Takahashi, "A simple inequality for the von Neumann-Jordan and James constants of a Banach space" 359 : 602-609, 2009