【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.更多还原

【Abstract】 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.更多还原