Several constants of Banach spaces and its application

Banach空间的几个常数及其应用

• 批准号: 16540142
• 负责人: SAITO Kichi-suke
• 金额: $ 2.37万
• 依托单位: Niigata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16540142/
• 关键词: Banach space; direct sum; uniform convexity; smoothness; Clarkson inequality; Hanner inequality; アブソリュートノルム; James定数; 狭義凸; 一様凸

The geometry of Banach space is an important and useful object in the every branch of Mathematics and has many applications. In particular, the form of the unit ball is important. From this, many geometrical notions of Banach spaces are arised. In this research, we study various constants of Banach spaces, for example, von Neumann-Jordan constant, James constant and so on. In particular, we studied the followings results in this study.(1) We considered Banach spaces defined by absolute norms and calculated the constants of special Banach spaces.An application, we studied the geometrical structure of Banach spaces.(2) We introduced the notion of ψ-direct sums of Banach spaces and we showed the necessary and sufficient conditions that the space is smooth and uniform smooth.(3) We in part calculated the James constant of 2-dimensional Lorentz space.(4) We characterized the uniform nonsquareness of ψ-direct sum of two Banach spaces.

Banach空间的几何形状是数学每个分支中的重要且有用的对象，并且具有许多应用。特别是，单位球的形式很重要。由此，出现了Banach空间的许多几何音符。在这项研究中，我们研究了Banach空间的各种常数，例如冯·诺曼 - 约旦常数，詹姆斯·康斯坦德等。特别是，我们研究了这项研究中的以下结果。（1）我们考虑了由绝对规范定义的BANACH空间，并计算了特殊的Banach空间的常数。我们研究了Banach空间的几何结构。（2）我们介绍了Banach空间和足够的条件的ψ-平稳的频率和平稳性的频率（3）的概念（3） （4）我们表征了两个Banach空间的单向总和的均匀非次数。

项目成果

The James constant of 2-dimensional Lorentz sequence spaces

二维洛伦兹序列空间的詹姆斯常数

• 发表时间: 2006
• 期刊: Bull.Kyushu Inst.Tech.Pure Appl.Math. 53
• 作者: 高橋泰嗣;高橋泰嗣;Tomonari Suzuki
• 通讯作者: Tomonari Suzuki

On strong random Clarkson inequality and strong Rademacher type

关于强随机克拉克森不等式和强拉德马赫型

• 发表时间: 2004
• 期刊: Bull.Kyushu Inst.Tech. Pure Appl.Math. 51
• 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
• 通讯作者: Yasutaka Yamada

Uniform non-squareness of ψ-direct sums of Banach spaces X_ψY

Banach 空间 X_ψY ψ 直和的一致非平方性

• 发表时间: 2004
• 期刊: Mathematical Inequalities and Applications 7
• 作者: Mikio Kato;Kichi-Suke Saito;Takayuki Tamura
• 通讯作者: Takayuki Tamura

Smoothness of ψ-direct sums of Banach spaces

Banach 空间 ψ 直和的平滑度

• 发表时间: 2005
• 期刊: Math.Inequal.Appl 8
• 作者: Mitani;Ken-ichi
• 通讯作者: Ken-ichi

Extensions 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: J.Nonlinear Conv.Anal. 6
• 作者: Yamada;Yasutaka
• 通讯作者: Yasutaka