一类缺项算子矩阵的四类点谱的扰动

PERTURBATION OF FOUR KINDS OF POINT SPECTRUMS OF A CLASS OF UPPER TRIANGULAR OPERATOR MATRICES

有界线性算子的点谱可进一步细分为4类,分别为σ_(p1),σ_(p2),σ_(p3)和σ_(p4).设H,K为无穷维可分的Hilbert空间,用M_C表示2×2上三角算子矩阵(OBAC),对于给定的A∈B(H),B∈B(K),描述了集合■C∈B(K,H)σ_(p1)(M_C),■C∈B(K,H)σ_(p2)(M_C),■C∈B(K,H)σ_(p3)(M_C)和■C∈B(K,H)σ_(p4)(M_C).

The point spectrum is divided into four kinds σp1,σp2,σp3 and σp4, In this paper, let H and K be two separable Hilbert spaces. Donote by Me the 2 x 2 upper triangular operator matrix acting on H ＋ K of the form （A C O B）.For given operators A∈B（H） and B ∈ B（K）, the sets