(n,k)-拟仿正规算子的广义Weyl型定理和谱的连续性

Generalized Weyl's theorem and spectral continuity for(n, k)-quasiparanormal operators

若T或T*是某可分Hilbert空间上的(n,k)-拟仿正规算子,则f(T)满足广义Weyl定理;进一步地,若T*是完全(n,k)-拟仿正规算子,则f(T)满足广义a-Weyl定理,其中f∈H(σ(T))满足在其定义域的每一个连通分支上是非常值的.最后,证明谱在(n,k)-拟仿正规算子类上是连续的.

If T or T^＊ is a totally （n, k）-quasiparanormal operator acting on an infinite dimensional separable Hilbert space, then we prove that generalized Weyl＇s theorem holds for f（T） for every f ∈H（σ（T）） which is nonconstant on each connected component of its domain. Moreover, if T^＊ is a totally （n, k）-quasiparanormal operator, then generalized a-Weyl＇s theorem holds for f（T） for every f ∈H（σ（T）） which is nonconstant on each connected component of its domain. Also, we prove that the spectrum is continuous on the class of all （n, k）-quasiparanormal operators.