对作用于一复可分无穷维Hilbet空间(？)上的两个有界线性算子T,S,它 们本性相似和π(T),π(S)(T,S在Calkin代数中的象)相似是否等价？这是有趣的问 题.本文引入一个算子类ES((？)),并证明了对ES((？))中的算子,上面提到的两种相 似性是等价的. 此外,还证明了ES((？))在B((?))中按照算子范数拓扑稠密.

For two operators acting on an infinite dimensional Hilbert space, it is interesting to investigate whether the essential similarity is equivalent to the similarity in the Calkin algebra. In this paper we introduce an operator class ES((?)), and show that, for two operators in ES((?)), the similarities above are the same. Moreover, we show that ES((?)) is dense in B((?)) in norm topology.