ALGEBRAIC SYSTEMS WHICH RELATE TO OPERATOR ALGEBRA AND RELATED TOPICS

首席研究员主要研究一个代数系统(Jordan三系)，它包括Jordan代数和算子代数作为其特例。特别地，他研究了Jordan三元系中特殊的三重积(二次积)与系统的代数结构之间的关系，得到了它们之间有很深的联系的事实。一个结果是，一个二次映射(保持二次积且不假定可加性)在JBW*-三元系的本质非交换部分上保持范数和整个实线性结构。一些结果已经发表，并有望有新的进展。研究人员高桥致力于交换Banach代数的研究。例如，他追溯了群代数的BSE定理的一个类比，并在交换Banach代数中找到了它的类比。他的一些成果已经在一些会议上曝光。然而，它们几乎都将在今年发表。研究者佐藤研究了Bernstein多项式，并检验了在几个不同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.