  We show that several known facts concerning roots of matrices generalize to
operator algebras and Banach algebras. We show for example that the so-called
Newton, binomial, Visser, and Halley iterative methods converge to the root in
Banach and operator algebras under various mild hypotheses. We also show that
the `sign' and `geometric mean' of matrices generalize to Banach and operator
algebras, and we investigate their properties. We also establish some other
facts about roots in this setting.
