[EN] We give the representations of (a + b)(d), (a + ab)(d) and (a + ba)(d) in terms of a, b, a(d) and b(d) being elements of a Banach algebra with a(3)b = ba and b(3)a = ab. We also give the representations of (a + b)(d) ...
[EN] Based on the conditions ab(2) = 0 and b pi(ab) is an element of A(d), we derive that (ab)(n), (ba)(n), and ab + ba are all generalized Drazin invertible in a Banach algebra A, where n is an element of N and a and b ...