Generalized B-Fredholm Banach algebra elements

• Published in: Mediterranean journal of mathematics Vol. 13; no. 5; pp. 3729 - 3746
• Main Authors: Cvetković, Miloš D., Boasso, Enrico, Živković-Zlatanović, Snežana Č.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01-10-2016; Springer Nature B.V
• Subjects: Banach spaces; Homomorphisms; Mathematics; Mathematics and Statistics; Perturbation; B-Fredholm element; Banach algebra; 47A55; 47A53; Perturbation class; 47A10; Homomorphism; 46H05; Generalized B-Fredholm element
• ISSN: 1660-5446; 1660-5454
• DOI: 10.1007/s00009-016-0711-y

Given a (not necessarily continuous) homomorphism between Banach algebras
T
:
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.