Extended Jacobson's lemma for the generalized inverse

Marjan Sheibani Abdolyousefi, Farzaneh Tayebi Semnani, Rahman Bahmani, Nahid Ashrafi

Abstract


In this paper, we present an extended Jacobson’s lemma for
g-Drazin inverse in Banach algebras. Let A be a Banach algebra, and let
a,b,c,d ∈ A satisfying
(ac)^2a = acdba = dbaca = (db)^2a;
(ac)^2d = acdbd = dbacd = (db)^2d.
Then 1−ac ∈ A^d if and only if 1−bd ∈ A^d. Related generalized Jacobson’s
lemma for Drazin, core and p-core inverses in a Banach algebra are thereby
obtained.


Refbacks

  • There are currently no refbacks.