An elementary analytical proof of the spectral radius formula (Q1272698)

The objective of this two pages article is to give an analytic proof of the spectral radius formula for Banach algebras using only elementary complex variable theory and the Hahn-Banach theorem for separable normed vector spaces. The proof does no use vector-valued integration or the Baire category theorem or the Gelfand representation theorem nor does it require Zorn's lemma.