k-拟-A算子的性质

Properties of k-quasi-A Operator

设T是无穷维可分的希尔伯特空间H上的k-拟-A算子,证明了T的B-Weyl谱满足谱映射定理.更重要,若T或T*是k-拟-A算子,则广义Weyl定理对T成立.另外,若T*是k-拟-A算子,则广义a-Weyl定理对T成立.

If T is a k-quasi- A operator acting on an infinite dimensional separable Hilbert space H, then it is proved that B-Weyl spectrum of T satisfies the spectral mapping theorem. Moreover, if T or T^＊ is a k -quasi- A operator, then generalized Weyl＇s theorem holds for T. Also, if T^＊ is an k-quasi-A operator, then generalized a-Weyl＇s theorem holds for T.