ALGEBRAIC SYSTEMS WHICH RELATE TO OPERATOR ALGEBRA AND RELATED TOPICS

与算子代数相关的代数系统及相关主题

• 批准号: 63540092
• 负责人: HAKEDA Josuke
• 金额: $ 1.02万
• 依托单位: YAMAGATA UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1988
• 资助国家: 日本
• 起止时间: 1988 至 1989
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63540092/
• 关键词: Jordan triple system; JBW* triple system; quadratic map; quadratic product; Banach algebra; BSE type theorem; Korovkin type theorem; Bernstein polynomial; Jordan三重系(Jordan triple systim); JBW^*(JBW^*triple systim); バナッハモジュ-ル(Banach module); Ser

Head investigator mainly worked on an ALGEBRAIC system (Jordan triple system) which include Jordan algebra and operator algebra as its special case. Especially, he researched the relationship between a special triple product (quadratic product) in a Jordan triple system and ALGEBRAIC structure of the system and had the fact that they are deeply related. One result is that a quadratic map (preserving quadratic product and not assuming additivity) preserves norm and the whole real linear structure on essentially non-commutative part of JBW*-triple system. Some results were already published and new progression will be expected.Investigator Takahashi worked on commutative Banach algebras. For instance, he traced on an analogy of BSE-theorem of group algebra and he had its analogue in commutative Banach algebra. Some results of him are already exposed at some conferences. However, almost of them will be published in this year.Investigator Sato studied Bernstein polynomial and checked the rate of convergence in a few different functional spaces.

首席研究员主要研究代数系统（乔丹三重系统），其中包括乔丹代数和算子代数作为其特例。特别是，他研究了Jordan三重系统中的一个特殊的三重积（二次积）与该系统的代数结构之间的关系，并发现它们之间存在深刻的联系。一个结果是二次映射（保留二次乘积且不假设可加性）保留了 JBW* 三重系统的本质上非交换部分上的范数和整个实数线性结构。一些结果已经发表，预计会有新的进展。高桥研究员致力于交换巴拿赫代数。例如，他追溯了群代数的 BSE 定理的类比，并在交换巴拿赫代数中得到了类似物。他的一些成果已经在一些会议上曝光了。不过，大部分都会在今年发表。佐藤研究员研究了伯恩斯坦多项式，并检查了几个不同函数空间中的收敛速度。

项目成果

KUNIO SATO: "RATE OF CONVERGENCE FOR BERNSTEIN POLYNOMIALS" SEMINAR OF REAL ANAL., 155-161, 1988.

KUNIO SATO：“伯恩斯坦多项式的收敛率”实分析研讨会，155-161，1988。

Sin-Ei Takahasi: "Commutative Banach algebras which satisfy a Bachner-Schoenberg-Eberlin type theorem" Proc.Amer.Muth.Soc.

Sin-Ei Takahasi：“满足 Bachner-Schoenberg-Eberlin 型定理的交换 Banach 代数”Proc.Amer.Muth.Soc。

渡利千波: 比実解析セミナー. 195-196 (1988)

Chinami Watari：刚性分析研讨会 195-196 (1988)。

羽毛田穰祐: "Jordan三重系とquadratic積" 日本数学会第28回実函数論・第27回函数解析学合同シンポジウム講演集録. 74-83 (1989)

Keisuke Haneda：“乔丹三重系统和二次积”日本数学会第28届实函数理论和第27届泛函分析联合研讨会论文集74-83（1989）。

SIN-EI TAKAHASI: "AN EXTENSION OF HELSON-EDWORDS THEOREM TO BANACH MODULES" INTERN. J. MATH. & APPL. MATH.

SIN-EI TAKAHASI：“HELSON-EDWORDS 定理对 BANACH 模的扩展”实习生。