约化代数的换位

本文找到了约化代数换位是自伴代数的几个充分条件。例如,如果有零空间是有限维的紧算子属于约化代数的换位u′,则u′是自伴代数。使用这些结果,可以得到约化算子问题的部分解答,特别我们推广了P.Rosenthal关于多项式紧的约化算子是正规算子的结果。

The Commutants of Reductive Algebras

This paper gives several sufficient conditions about the comm-utant of a reductive algebra is a selfadjoint algebra. For example, if zero-space is the commutant u' of finitely dimensional compact operators belonging to a reductive algebra, u' is a self-adjoint algebra. From these results, partly answers to the questions of reductive algebra can be obtained. Especially we extend the result by P. Rosenthal that reductive operators of compact for polynomial are normal operators.