上三角算子矩阵的谱摄动

Perturbations of the spectra of upper triangular operator matrices

研究了Hilbert空间上上三角算子矩阵的Kato下半Fredhol m谱.利用上三角算子矩阵中对角线上两个算子的零度和亏数之间的关系,给出了上三角算子矩阵为Kato下半Fredholm算子的充分条件:若算子B为Kato下半Fredhol m算子且n(B)=∞,则存在算子C,使得MC=A C0B为Kato下半Fredholm算子;同时研究了上三角算子矩阵的Kato下半Fredholm谱的摄动,得到了:若对任意λ∈σ(B),B*-λI是Saphar算子且d(B*-λI)=∞,则∩C∈B(K,H)σlk(MC)=σlk(B)∪{λ∈C:A-λI是紧的}∪(σlk(A)∩ρ(B))=σSF-(B)∪{λ∈C:A-λI是紧的}∪(σlk(A)∩ρ(B)).

The Kato lower semi-Fredholm spectrum of an upper triangular operator matrix on a Hilbert space is discussed.By means of the relationship between n(T) and d(T) of two operators on the diagonal of an upper triangular operator matrix,some sufficient conditions for an upper triangular operator matrix to be a Kato lower semi-Fredholm operator are given.It is proved that if B is a Kato lower semi-Fredholm operator and n(B)=∞,then MC=AC 0B is a Kato lower semi-Fredholm operator for some operator C.Meanwhile,the p...