Eigenelements of perturbed operators

Journal of the Australian Mathematical Society

B. V. Limaye¹ 

[1] M. T. Nair

关键词: 47 A 55;    47 A 70;    47 A 10;    41 A 35;   

DOI  :  10.1017/S1446788700030299

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

Let λ0 be a semisimple eigenvalue of an operator T0. Let Γ0 be a circle with centre λs0 containing no other spectral value of T0. Some lower bounds are obtained for the convergence radius of the power series for the spectral projection P(t) and for trace T(t)P(t) associated with linear perturbation family T(t) = T0 + tV0 and the circle Γ0. They are useful when T0 is a member of a sequence (Tn) which approximates an operator T in a collectively compact manner. These bounds result from a modification of Kato's method of majorizing series, based on an idea of Redont. I λ0 is simple, it is shown that the same lower bound are valid for the convergence radius of a power series yielding an eigenvector of T(t).

【 授权许可】

Unknown