On some classes of Saphar type operators

被引：0
|
作者：
Snežana Č. Živković-Zlatanović
Slaviša V. Djordjević
机构：
[1] University of Niš,Faculty of Sciences and Mathematics
[2] Benemérita Universidad Autónoma de Puebla,undefined
[3] Facultad de Ciencias F’indsico Matemáticas,undefined
来源：
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | 2022年 / 116卷
关键词：
Banach space; Quasi–Fredholm operators; Saphar operators; Left and right Fredholm operators; Left and right Weyl operators; Left and right Drazin invertible operators; Spectrum; 47A53; 47A10;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper we define and study operators of Saphar type in a Banach space, their subclasses, essentially left (right) Drazin invertible operators and left (right) Weyl–Drazin invertible operators, by means of kernels and ranges of powers of an operator. A bounded linear operator T on a Banach space X is said to be of Saphar type if T is a direct sum of a Saphar operator and a nilpotent one. We prove that T is essentially left (right) Drazin invertible if and only if T is a direct sum of a left (right) Fredholm operator and a nilpotent one, as well as that T is left (right) Weyl–Drazin invertible if and only if T is a direct sum of a left (right) Weyl operator and a nilpotent operator. We also consider the corresponding spectra.
引用
收藏
相关论文
共 50 条
12345