上三角算子矩阵的(α,β)-本质谱

On the (α,β)-Essential Spectrum of Upper Triangular Operator Matrices

设■和■为可分的无穷维Hilbert空间.对于给定的算子A∈■(■)和B∈■(■),本文给出存在(和所有)C∈■(■,■),使得(A0CB)为(α,β)-半Fredholm算子的充分必要条件.此外,得到了相关结论.

Let■and■ be separable infinite dimensional Hilbert spaces,and let A G■(■) and B ∈■(■) be given operators.A necessary and sufficient condition is obtained for(A0CB) to be an(α,β)-semi-Fredholm operator for some(respectively,all)C ∈■(■,■).Furthermore,some related results are obtained.