2003 Fiscal Year Annual Research Report

バナッハ空間及び関数空間の幾何学的構造の研究とその応用

Research Project

Project/Area Number	14540181
Research Institution	Kyushu Institute Of Technology
Principal Investigator	加藤幹雄九州工業大学, 工学部, 教授 (50090551)
Co-Investigator(Kenkyū-buntansha)	斎藤吉助新潟大学, 理学部, 教授 (30018949) 高橋泰嗣岡山県立大学, 情報工学部, 教授 (30001853) 岡崎悦明九州工業大学, 情報工学部, 教授 (40037297)
Keywords	absolute norm / convex function / ψ-direct sum of Banach spaces / sharp uniform convexity / type-cotype / strong type-cotype / norm inequality / Banach space
Research Abstract	1.Banach空間のψ-直和について: (1)uniformly non-^n_1であるための必要十分条件を与えた。 (2)reflexivity, super-reflexivity, weak nearly uniform smoothness(不動点性に関係),smoothness等を特徴付けた。 (3)R^2上のabsolute normのJames定数を,未決定ないくつかの場合に決定した。 2.Type,cotypeの概念の拡張とrandom Clarkson型不等式の関係について考察し,次の成果を得た。 (1)Strong random Clarkson不等式を導入,この不等式の成り立つBanach空間をstrong type p,またp-uniformly smoothな空間として特徴付けた。この不等式のLebesgue-Bochner空間L_r(X)への遺伝性を示した。 (2)Strong random Clarkson不等式を拡張して(1)の結果を精密化した。 3.Hanner型不等式を考察,とくにoptimal 2-uniform convexityとの関係を明らかにした。また,重みつきHanner型不等式,その多元版を考察して一定の知見を得た。 4.以上の成果について,日本数学会秋季総合分科会・年会,数理解析研究所研究集会,実解析学シンポジウム等,また,Wladyslaw Orlicz Centenary Conference and Function Spaces VII(Poznan, Poland)で発表,同「Geometry of Banach spaces」分科会で座長を務めた。

Research Products

(12 results)

All Other

All Publications (12 results)

[Publications] Ken-ichi Mitani: "The James constant of absolute norms on R^2"Journal of Nonlinear and Convex Analysis. 4. 399-410 (2003)
[Publications] Mikio KATO: "On ψ-direct sums of Banach spaces and convexity"Journal of the Australian Mathematical Society. 75. 413-422 (2003)
[Publications] Ken-ichi Mitani: "Smoothness of absolute norms on C^n"Journal of Convex Analysis. 10. 89-107 (2003)
[Publications] Yasutaka YAMADA: "On strong random Clarkson inequality and strong Rademacher type"Bulletin of the Kyushu Institute of Technology Pure and Applied Mathematics. 51. 1-15 (2004)
[Publications] Yasuji TAKAHASHI: "Hanner-type inequality and uniform non-squareness for Banach spaces"Hokkaido University Technical Report Series in Mathematics. 80. 60-63 (2004)
[Publications] Mikio KATO: "Uniform non-squareness of ψ-direct sums of Banach spaces X【symmetry】_ψY"Mathematical Inequalities and Applications. (発表予定).
[Publications] Yasutaka YAMADA: "Hanner-type inequality and optimal 2-uniform convexity and smoothness inequalities"京都大学数理解析研究所講究録. (発表予定).
[Publications] Yasuji TAKAHASHI: "On Hanner-type inequality in Banach spaces"Proceedings of International Symposium on Banach and Function Spaces 2003. (発表予定).
[Publications] Takayuki TAMURA: "A geometric condition on related to fixed point property in ψ-direct sums of Banach spaces X【symmetry】_ψY"Proceedings of International Symposium on Banach and Function Spaces 2003. (発表予定).
[Publications] Sin-Ei Takahashi: "Convex sets and inequalities"Archives of Inequalities and Applications. (発表予定).
[Publications] Makoto Tsukada: "On Wirtinger-Beesak type integral inequalities"Proceedings of the 3rd International Conference on Nonlinear Analysis and Convex Analysis. (発表予定).
[Publications] Ken-ichi Mitani: "Smoothness of ψ-direct sums of Banach spaces"Mathematical Inequalities and Applications. (発表予定).

2003 Fiscal Year Annual Research Report

バナッハ空間及び関数空間の幾何学的構造の研究とその応用

Principal Investigator

加藤 幹雄 九州工業大学, 工学部, 教授 (50090551)

Research Products

[Publications] Ken-ichi Mitani: "The James constant of absolute norms on R^2"Journal of Nonlinear and Convex Analysis. 4. 399-410 (2003)

[Publications] Mikio KATO: "On ψ-direct sums of Banach spaces and convexity"Journal of the Australian Mathematical Society. 75. 413-422 (2003)

[Publications] Ken-ichi Mitani: "Smoothness of absolute norms on C^n"Journal of Convex Analysis. 10. 89-107 (2003)

[Publications] Yasutaka YAMADA: "On strong random Clarkson inequality and strong Rademacher type"Bulletin of the Kyushu Institute of Technology Pure and Applied Mathematics. 51. 1-15 (2004)

[Publications] Yasuji TAKAHASHI: "Hanner-type inequality and uniform non-squareness for Banach spaces"Hokkaido University Technical Report Series in Mathematics. 80. 60-63 (2004)

[Publications] Mikio KATO: "Uniform non-squareness of ψ-direct sums of Banach spaces X【symmetry】_ψY"Mathematical Inequalities and Applications. (発表予定).

[Publications] Yasutaka YAMADA: "Hanner-type inequality and optimal 2-uniform convexity and smoothness inequalities"京都大学数理解析研究所講究録. (発表予定).

[Publications] Yasuji TAKAHASHI: "On Hanner-type inequality in Banach spaces"Proceedings of International Symposium on Banach and Function Spaces 2003. (発表予定).

[Publications] Takayuki TAMURA: "A geometric condition on related to fixed point property in ψ-direct sums of Banach spaces X【symmetry】_ψY"Proceedings of International Symposium on Banach and Function Spaces 2003. (発表予定).

[Publications] Sin-Ei Takahashi: "Convex sets and inequalities"Archives of Inequalities and Applications. (発表予定).

[Publications] Makoto Tsukada: "On Wirtinger-Beesak type integral inequalities"Proceedings of the 3rd International Conference on Nonlinear Analysis and Convex Analysis. (発表予定).

[Publications] Ken-ichi Mitani: "Smoothness of ψ-direct sums of Banach spaces"Mathematical Inequalities and Applications. (発表予定).

加藤幹雄九州工業大学, 工学部, 教授 (50090551)