The norm structure of Banach spaces and its application.

Banach空间的范数结构及其应用。

• 批准号: 14540160
• 负责人: SAITO Kichi-suke
• 金额: $ 2.3万
• 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: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540160/
• 关键词: Banach space; uniform convex; strict convex; von Neumann-Jordan constant; James constant; ノルム; Banach空間; absolute norm; 一様凸性; 狭義凸性; smoothness

The study of Banach space theory is an important and useful object in the every branch of Mathematics and has many applications. In this Research, we study the rotundity and the nonsquareness of unit balls of Banach spaces. In particular, we attempt to study the absolute norms of C^n.(1)At first, we defined the 4-direct sum of two Banach spaces and we showed the necessary and sufficient conditions that the space is strictly convex(resp.uniform convex).(2)We proved the necessary and sufficient conditions that the absolute norm on C^n is smooth.(3)We have the formulae of the James constant of absolute normed space on R^2 and we apply the Lorentz space.(4)We study the uniform nonsquareness of C^n. We showed the uniform nonsquareness of 4-direct sum of two Banach spaces.In the near future, we study the geometrical structure of the infinite dimensional Banach spaces, in particular, Schatten p-class operators c_p, Orliz space, noncommutativeL^p-space and so on.

Banach空间理论的研究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。在这项研究中，我们研究了Banach空间的单位球的旋转率和非测量。特别是，我们尝试研究C^n的绝对规范（1）首先，我们定义了两个Banach空间的4个直接总和，我们显示了必要和充分的条件，即严格凸出空间（spess.均匀的凸面）。（2）我们证明了必要的和足够的条件，我们证明了我们在c^n上的绝对规范，我们的oss and and and and and n of c^n是平稳的（3）。 Lorentz空间。（4）我们研究了C^n的均匀非质量。我们展示了两个Banach空间的4个方向总和的均匀非质量。在不久的将来，我们研究了无限尺寸Banach空间的几何结构，尤其是Schatten P级操作员C_P，Orliz Space，noncommutatativel^p Pass等。

项目成果

Mikio Kato: "On 4-direct sums of Banach spaces and convexity"J.Australian Mathematical Society. 75. 413-422 (2003)

加藤干雄：“论巴拿赫空间和凸性的 4-直和”J.澳大利亚数学会。

Ohwada, Tomoyoshi: "Factorization in analytic crossed products"J. Math. Soc. Japan. 54・1. 21-33 (2002)

大和田智吉：“分析交叉乘积的因式分解”J.Soc. 21-33。

Yasuji Takahashi: "Strict convexity of absolute norms on C^2 and direct sums of Banach spaces"J.Inequalities and Applications. 7. 179-186 (2002)

Yasuji Takahashi：“C^2 上绝对范数的严格凸性和 Banach 空间的直和”J.不等式与应用。

Kato, Mikio: "On 4-direct sums of Banach spaces"J. Australian Math. Soc.. (発表予定).

Kato, Mikio：“关于 Banach 空间的 4 直和”J. Australian Math Soc..（待提交）。

Takahashi, Yasuji: "On sharp uniform convexity, smoothness, and strong type, cotype inequalities"J. nonlinear convex Analysis. 3・2. 267-281 (2002)

Takahashi Yasuji：“关于锐均匀凸性、平滑性和强型、共型不等式”J. 3・2。