Banach代数中Fredholm型元及其谱理论  

Fredholm-type element and its spectrum theory in Banach algebras

作　　者：孔莹莹 蒋立宁 KONG Yingying;JIANG Lining(School of Mathematics and Statistics,Beijing Institute of Technology,100081,Beijing,PRC)

机构地区：[1]北京理工大学数学与统计学院,北京市100081

出　　处：《曲阜师范大学学报（自然科学版）》2022年第3期33-44,共12页Journal of Qufu Normal University(Natural Science)

基　　金：国家自然科学基金(11871303).

摘　　要：文章概述了Banach代数中Fredholm型元及其谱理论.以Fredholm算子及其谱理论为原型,介绍了Fredholm型算子及其谱理论,研究了Banach代数中的Fredholm型元及其Fredholm理论.进一步探讨了Banach代数中和代数同态相关的Fredholm理论、Fredholm族及其指标理论和C^(*)-代数的Fredholm模等.This paper refines and summarizes the developments of Fredholm-type elements and its spectrum theory.Based on Fredholm operators and its spectrum theory,Fredholm-type operators and its spectrum theory are introduced.Fredholm-type elements in Banach algebras and its spectral theory are studied.Furthermore,the new trend of Fredholm-type elements and its spectrum theory is presented,including Fredholm theory with respect to Banach algebra homomorphism;Fredholm family and its analytic index and Fredholm module of C^(*)-algebra and so on.

关 键 词：Fredholm型元 谱 Fredholm理论 BANACH代数 指标 

分 类 号：O177.2[理学—数学]