Generalized B-Fredholm Banach algebra elements

2015/04/12 by Cvetkovic, Milos D., Boasso, Enrico, Zivkovic-Zlatanovic, Snezana C.
#47A10 #47A55 47A5 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46H05 #Secondary 47A53

paper · doi:10.48550/arxiv.1504.02952

Abstract

Given a (not necessarily continuous) homomorphism between Banach algebras \T\colon\A→\B, an element a∈\A will be said to be B-Fredholm (respectively generalized B-Fredholm) relative to \T, if \T(a)∈ \B is Drazin invertible (respectively Koliha-Drazin invertible). In this article, the aforementioned elements will be characterized and their main properties will be studied. In addition, perturbation properties will be also considered.

Related

• B-Fredholm Elements in Rings and Algebras
• On Classes of Fredholm Type Operators
• Isolated spectral points and Koliha-Drazin invertible elements in quotient Banach algebras and homomorphism ranges
• One-sided Drazin inverses in Banach algebras and perturbations of B-Fredholm spectra
• B-Fredholm theory in Banach algebras