非自伴的对称闭算子在扰动下的谱

Spectrum of non-self-adjoint closed symmetric operation with perturbation

对于Hilbert空间H上的非自伴的对称闭算子A,在其扰动算子B是对称算子且关于A的相对界小于1/2的条件下,利用对称闭算子的亏指数和自伴算子的扰动定理,证明了扰动后的算子A+B的谱等于算子A的谱.

Let A be the non-self-adjoint closed symmetric operation on a Hilbert space, H and B be the perturbed operation of A. Assume that B is symmetrical and its relative boundary about A is smaller than 1/2. Using perturbation theorems of self-adjoint operations and the deficiency indies of closed symmetric operations, it is proved that the spectral sef σ （ A ＋ B）of the operation A＋B equals to the spectral set σ （ A）of the operation A.