Nest代数的某些范数闭理想

Some Norm Closed Ideals in Nest Algebras

设Ｒ＿Ｎ是Ｎｅｓｔ代数ａｌｇＮ的Ｊａｃｏｂｓｏｎ根，用表示由；生成的ａｌｇＮ的范数闭双边理想。Ｊ．Ｒ．Ｒｉｎｇｒｏｓｅ［１，定理５．４］给出了Ｒ＿Ｎ的Ｋ１ｎｇｒｏｓｅ特征，本文将给出具有广义Ｒｉｎｇｒｏｓｅ特征的充分必要条件。

Let R_N be the Jacobson radical of the nest algebra algN, we write for the normclosed two- sided ideal generated by the set R￣n ={T_1T_2…T_n.J . R. Ringrose[1, Theorem 5. 4 ] obtained the character of the Jacobson radical R_N . In this paper,we give an “if and only if ”that has the generalized Ringrose character.