摘要
设A,B是Hilbert空间H上的算子,定义B(H)上的算子τ=τ(A,B),J=J(A,B)为τ(X)=AX-XB,J(X)=AXB-X。本文求得了算子J的近似点谱、剩余谱,给出了J的值域在B(H)中按范数拓扑稠密的充要条件,推广了Fialkow的结果。
For operators A and B on a Hilbert space H, let τ=τ(A,B) and J=J (A,B) de-note the operators on B(H) defined by τ(X)=AX-XB,J(X)=AXB-X, respec-tively. Let J be the induced operator on the Calkin algebra (?)(H). The spectrumanalysis of operators J and J is given. The characterization of the norm densenessof the range of J in B(H) is also given. Some results on τ(A,B) are extened toJ(A,B).
出处
《复旦学报（自然科学版）》
CAS
CSCD
北大核心
1989年第2期148-154,共7页
Journal of Fudan University：Natural Science
