线性算子束的稳定半径
The stability radius of linear operator pencils
摘要：
设T和S是从巴拿赫空间X到Y的两个有界线性算子，T是Fredholm，稳定数k（T;S）为0.设d（T;S）是所有r > 0的上确界，使得dim N（T-λS）和codim R（T-λS）对所有λ都是常数，|λ| < r. 1980年H. Bart和D.C. Lay证明了d（T;S）= \lim_{n\to\infty} γ_{n}（T;S）^{1/n}，其中γ_{n}（T;S）是某些非负的（扩展的）实数.对于X=Y和S = I，恒等算子，我们有γ_{n}（T;S）= γ（T^n），其中γ是约化最小模。本文用T的广义逆的谱半径给出了稳定半径的另一种表示。还考虑了Fredholm线性丛的广义预解式的存在性。
英文摘要：
Let T and S be two bounded linear operators from Banach spaces X into Y and suppose that T is Fredholm and the stability number k(T;S) is 0. Let d(T;S) be the supremum of all r > 0 such that dim N(T-λS) and codim R(T-λS) are constant for all λwith |λ| < r. It was proved in 1980 by H. Bart and D.C. Lay that d(T;S) = \lim_{n\to\infty}γ_{n}(T;S)^{1/n}, where γ_{n}(T;S) are some non-negative (extended) real numbers. For X=Y and S = I, the identity operator, we have γ_{n}(T;S) = γ(T^n), where γis the reduced minimum modulus. A different representation of the stability radius is obtained here in terms of the spectral radii of generalized inverses of T. The existence of generalized resolvents for Fredholm linear pencils is also considered.
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