套代数理想的距离公式

The Distance Formulas of Some Ideals of Nest Algebras

设Ｎ是Ｈｉｌｂｅｒｔ空间Ｈ上的一个完备套，是Ｎ上的标准谱测度．本文给出了Ｈ上任一有界线性算子Ｔ到套代数Ａｌｇ Ｎ的Ｌａｒｓｏｎ理想ＲＮ的距离公式为ＡｌｇＮ的半根理想，则ｄ（Ｔ，ＲＮ）＝ｓｕｐ｛ｉＮ（Ｔ）：Ｎ｝．

Let N be a complete nest over a Hilbert space H, and e be a natural spectralmeasure on N. Then the distance from an arbitrary operator T in B(H) to RN, theLarson ideal of the nest algebra AlgN, is given by d(T,RN) where 0 for all N e N}, the semi-radical ideal of Alga, then d(T, V) = sup{IN(T): N