ALGEBRAIC SYSTEMS WHICH RELATE TO OPERATOR ALGEBRA AND RELATED TOPICS

首席研究员主要研究了一种以约当代数和算子代数为特例的代数系统。特别是，他研究了Jordan三重系统中一个特殊的三重积（二次积）与该系统的代数结构之间的关系，并得出了两者之间的深刻联系。一个结果是在JBW*-三重系统的本质非交换部分上，二次映射（保留二次积而不假设可加性）保留范数和整个实线性结构。一些研究结果已经发表，预计会有新的进展。研究者Takahashi研究交换巴拿赫代数。例如，他对群代数的bse定理进行了类比，并在交换巴拿赫代数中得到了类比。他的一些成果已经在一些会议上曝光。然而，他们中的大部分将在今年出版。研究者Sato研究了Bernstein多项式，并检验了它在几个不同的函数空间中的收敛速度。

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.