RESEARCH ON STRUCTURE THEORY OF BANACH SPACES AND NORM INEQUALITIES WITH APPLICATIONS

Banach空间结构理论及范数不等式研究及其应用

• 批准号: 15540179
• 负责人: TAKAHASHI Yasuji
• 金额: $ 2.3万
• 依托单位: OKAYAMA PREFECTURAL UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540179/
• 关键词: Hanner type inequality; Random Clarkson inequality; Norm inequality; Geometry of Banach spaces; Schaffer type constant; Uniform non-squareness; normal structure coefficient; ψ-direct sums of Banach spaces; Geometry of Banach spaces; Hanner type i

In this research we considered some generalizations and refinements of classical norm inequalities and geometric constants, and investigated geometric properties of Banach spaces X in connection with those inequalities and constants. In particular, we considered refined generalizations of Hanner inequality and Schaffer constant, and characterized geometric properties of X in terms of these inequalities and constants. We also investigated geometric properties of ψ-direct sums of Banach spaces.The main results are stated as follows :1. Norm inequalities and geometry of Banach spacesWe consider some refined generalizations of Hanner's inequality for Banach spaces X, and characterize geometric properties of X such as uniform non-squareness, p-uniform smoothness and quniform convexity in terms of these inequalities. We also consider extensions of strong random Clarkson inequalities, and characterize Banach spaces of strong type p in terms of those inequalities.2. Refined generalizations of Schaffer constant and geometry of Banach spacesWe introduce new geometric constants (or functions) φx(τ) for Banach spaces X as refined generalizations of the Schaffer constant S(X), and investigate some geometric properties of X in terms of these constants (or functions). In particular, the normal structure coefficients N(X) of X can be estimated by φx(τ). Some examples of concrete Banach spaces X with the calculation of φx(τ) are also given.3. Geometric properties of ψ-direct sums of Banach spacesWe consider the ψ-direct sum (X_1 【symmetry】 X_2 【symmetry】 【triple bond】 【symmetry】 X_n)_ψ of Banach spaces X_1, X_2, 【triple bond】, X_n, and investigate geometric properties such as uniform non-squareness, uniform convexity, uniform non-l^n_1-ness (B_n-convexity) and fixed point properties. These properties of such spaces can be described in terms of the function ψ and Banach spaces X_1,X_2,【triple bond】, X_n.

本文考虑了经典的范数不等式和几何常数的推广和加细，并结合这些不等式和几何常数研究了Banach空间X的几何性质。特别地，我们考虑了Hanner不等式和Schaffer常数的精化推广，并利用这些不等式和常数刻画了X的几何性质。我们还研究了Banach空间的n-直和的几何性质，主要结果如下：1。Banach空间的范数不等式与几何考虑了Banach空间X上Hanner不等式的一些精化推广，并利用这些不等式刻画了X的一致非平方性、p-一致光滑性和q-一致凸性等几何性质。我们还考虑了强随机克拉克森不等式的推广，并利用这些不等式刻画了强p型Banach空间. Schaffer常数的精化推广与Banach空间的几何我们在Banach空间X中引入了新的几何常数（或函数）φx（τ）作为Schaffer常数S（X）的精化推广，并利用这些常数（或函数）研究了X的一些几何性质.特别地，X的正规结构系数N（X）可以通过φx（τ）来估计。给出了具体Banach空间X中φx（τ）的计算实例. Banach空间的ψ-直和的几何性质我们考虑Banach空间X_1、X_2、[三键]、X_n的ψ-直和（X_1 [对称性] X_2 [对称性] [三键] [对称性] X_n）_ψ，并研究了一致非方形性、一致凸性、一致非l ^n_1性（B_n-凸性）和不动点性质等几何性质。这类空间的这些性质可以用函数λ和Banach空间X_1，X_2，[三键]，X_n来描述。

项目成果

Extension of random and strong random Clarkson inequalities in Banach spaces

Banach 空间中随机和强随机克拉克森不等式的推广

• 发表时间: 2005
• 期刊: Journal of Nonlinear and Convex Analysis 6
• 作者: 高橋泰嗣;高橋泰嗣;Tomonari Suzuki;Yasuji Takahashi;Yasuji Takahashi;Tomonari Suzuki;Yasutaka Yamada;加藤幹雄;Jyunji Inoue;Lasha Ephremidze;Hiroyuki Takagi;Hiroyuki Takagi;山田康隆;高木康啓行;Sin-Ei Takahasi;山田康隆;田村高幸;田村高幸;高橋泰嗣;Takeshi Miura;Yasutaka Yamada
• 通讯作者: Yasutaka Yamada

Vector valued ergodic theorems for multiparameter additive processes II

多参数加性过程的向量值遍历定理 II

• 发表时间: 2003
• 期刊: Colloquium Mathematicum 97
• 作者: T.Aoki;T.Kawai;T.Koike;Y.Takei;S.Kamiya;Tatsuhiro Honda;Makoto Sakai;Ryotaro Sato
• 通讯作者: Ryotaro Sato

Strong random Clarkson inequality and its extension

强随机克拉克森不等式及其推广

• 发表时间: 2004
• 期刊: 京都大学数理解析研究所講究録 1396
• 作者: 高橋泰嗣;高橋泰嗣;Tomonari Suzuki;Yasuji Takahashi;Yasuji Takahashi;Tomonari Suzuki;Yasutaka Yamada;加藤幹雄;Jyunji Inoue;Lasha Ephremidze;Hiroyuki Takagi;Hiroyuki Takagi;山田康隆;高木康啓行;Sin-Ei Takahasi;山田康隆;田村高幸;田村高幸;高橋泰嗣;Takeshi Miura;Yasutaka Yamada;Makoto Tsukada;Yasutaka Yamada;Hiroyuki Takagi;Yasutaka Yamada;Takayuki Tamura;Takayuki Tamura;Yasuji Takahashi;Takeshi Miura;Makoto Tsukada;山田康隆;Takeshi Miura;山田康隆;山田康隆;高橋泰嗣;Yasutaka Yamada;山田康隆
• 通讯作者: 山田康隆

Hyers-Ulam stability constants of first order linear differential operators

一阶线性微分算子的 Hyers-Ulam 稳定性常数

• 发表时间: 2004
• 期刊: Journal of Mathematical Analysis and Applications 296
• 作者: 高橋泰嗣;高橋泰嗣;Tomonari Suzuki;Yasuji Takahashi;Yasuji Takahashi;Tomonari Suzuki;Yasutaka Yamada;加藤幹雄;Jyunji Inoue;Lasha Ephremidze;Hiroyuki Takagi;Hiroyuki Takagi;山田康隆;高木康啓行;Sin-Ei Takahasi;山田康隆;田村高幸;田村高幸;高橋泰嗣;Takeshi Miura;Yasutaka Yamada;Makoto Tsukada;Yasutaka Yamada;Hiroyuki Takagi;Yasutaka Yamada;Takayuki Tamura;Takayuki Tamura;Yasuji Takahashi;Takeshi Miura;Makoto Tsukada;山田康隆;Takeshi Miura;山田康隆;山田康隆;高橋泰嗣;Yasutaka Yamada;山田康隆;高橋泰嗣;Ryotaro Sato;Sin-Ei Takahasi
• 通讯作者: Sin-Ei Takahasi

Solvability of the functional equation f=(T-I)h for vector-valued functions

向量值函数的函数方程 f=(T-I)h 的可解性

• 发表时间: 2004
• 期刊: Colloq.Math. 99
• 作者: 高橋泰嗣;高橋泰嗣;Tomonari Suzuki;Yasuji Takahashi;Yasuji Takahashi;Tomonari Suzuki;Yasutaka Yamada;加藤幹雄;Jyunji Inoue;Lasha Ephremidze;Hiroyuki Takagi;Hiroyuki Takagi;山田康隆;高木康啓行;Sin-Ei Takahasi;山田康隆;田村高幸;田村高幸;高橋泰嗣;Takeshi Miura;Yasutaka Yamada;Makoto Tsukada;Yasutaka Yamada;Hiroyuki Takagi;Yasutaka Yamada;Takayuki Tamura;Takayuki Tamura;Yasuji Takahashi;Takeshi Miura;Makoto Tsukada;山田康隆;Takeshi Miura;山田康隆;山田康隆;高橋泰嗣;Yasutaka Yamada;山田康隆;高橋泰嗣;Ryotaro Sato;Sin-Ei Takahasi;Mikio Kato;Yasuji Takahashi;Yasutaka Yamada;Yasuji Takahashi;Yasutaka Yamada;Sin-Ei Takahashi;Ryotaro Sato
• 通讯作者: Ryotaro Sato