On the differences of the consecutive powers of Banach algebra elements
On the differences of the consecutive powers of Banach algebra elements
Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence ${x^{n}(x-1)}_{n ∈ ℕ}$ for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstanc