A New Geometric Constant in Banach Spaces Related to the Isosceles Orthogonality
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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.
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 (25)
- M. Brodskii, "On the center of a convex set", Doklady Akad. Nauk SSSR (N.S.), 59, pp.837~840 (1948)
- G. Birkhoff, "Orthogonality in linear metric spaces", Duke Math. J, 1, pp.169~172 (1935)
- C. Bentez, "Characterization of inner product spaces through rectangle and square inequalities", Rev. Roumaine Math. Pures Appl, 29, pp.543~546 (1984)
- V. Balestro, "Angles in normed spaces", Aequat. Math, 91, pp.201~236 (2017)
- J. A. Clarkson, "Uniformly convex spaces", Trans. Amer. Math. Soc, 40, pp.396~414 (1936)
- J. A. Clarkson, "The von Neumann-Jordan constant for the Lebesgue space", Ann. of Math, 38, pp.114~115 (1937)
- Y. Cui, "Some properties concerning Milman’s moduli", J. Math. Anal. Appl, 329, pp.1260~1272 (2007)
- M. M. Day, "Uniform convexity in factor and conjugate spaces", Ann. of Math, 45, pp.375~385 (1944)
- S. Dhompongsa, "On a generalized James constant", J. Math. Anal. Appl, 285, pp.419~435 (2003)
- K. Goebel, "Convexity of balls and fixed point theorems for mapping with non-expansive square", Compositio Math, 22, pp.269~274 (1970)
- J. Gao, "On the geometry of spheres in normed linear spaces", J. Austral. Math. Soc. Ser. A, 48, pp.101~112 (1990)
- C. Hao, "Homogeneity of isosceles orthogonality and related inequal-ities", J. Inequal. Appl, 84, pp.9~ (2011)
- R. C. James, "Uniformly non-square Banach spaces", Ann. of Math, 80, pp.542~550 (1964)
- R. C. James, "Orthogonality in normed linear spaces", Duke Math. J, 12, pp.291~302 (1945)
- D. Ji, "Quantitative characterization of the difference between Birkhofforthogonality and isosceles orthogonality", J. Math. Anal. Appl, 323, pp.1~7 (2006)
- P. Jordan, "On inner products in linear metric spaces", Ann. Math. J, 36, pp.719~723 (1935)
- J. Lindenstrauss, "On the modulus of smoothness and divergent series in Ba-nach spaces", Michigan Math. J, 10, pp.241~252 (1963)
- H. Mizuguchi, "The constants to measure the differences between Birkhoffand isosceles orthogonalities", Filomat, 30, pp.2761~2770 (2015)
- P. L. Papini, "Measurements of differences between orthogonality types", J. Math. Anal. Appl, 397, pp.285~291 (2013)
- L. Qi, "New geometric constants of isosceles orthogonal type", e-print arXiv: 2111.08392, ~
- B. D. Roberts, "On the geometry of abstract vector spaces", Tohoku Math, 39, pp.42~59 (1934)
- Y. Takahashi, "Von Neumann-Jordan constant and uniformly non-square Banach spaces", Nihonkai Math. J, 9, pp.155~169 (1998)
- Y. Takahashi, "A simple inequality for the von Neumann-Jordan and James constants of a Banach space", J. Math. Anal. Appl, 359, pp.602~609 (2009)
- F. Wang, "Some inequalities concering the James constant in Ba-nach spaces", J. Math. Anal. Appl, 353, pp.305~310 (2009)
- C. Yang, "On estimates of the generalized Jordan-von Neumann constant of Banach spaces", JIPAM. J. Inequal. Pure Appl. Math, 7, pp.1~5 (2006)