算子序列的升标和降标

THE ASCENT AND DESCENT OF OPERATOR SEQUENCES

本文研究了与算子紧序列有关的一类算子序列和算子上半Fredholm序列的升标和降标的一些性质.利用同伦的思想证明了具有有限升标(降标)的算子上半Fredholm序列在其摄动类中交换元的摄动下具有同样性质,从而把单个半Fredholm算子的有关结果推广到算子序列.

In this paper, we study some properties of a class of operator sequences which is related to collectively compact operator sequences and operator upper-semi Fredholm sequences, and we prove that the collection of operator upper-semi Fredholm sequences with finite ascent（descent） is closed under commuting operator sequences perturbation class associated with them according to the thought of homotopy, which is a generalization of the results under semi-Fredholm operator conditions.