Spectral Inclusion and Analytic Continuation
Aharon Atzmon, Alexandre Erëmenko, Mikhail Sodin · Bulletin of the London Mathematical Society · 1999
Let a be an element in a complex Banach algebra with unit, and let r be a nonnegative number. The Gelfand spectral radius formula implies that the spectrum of a is included in the disk {z ∈ C: |z| ⩽ r} if and only if lim n → ∞ ‖ a n ‖ 1 / n ⩽ r . 1991 Mathematics Subject Classification 46H99, 47A10, 30B40.