Norms on unitizations of Banach algebras

Abstract

Equivalence of various norms on the unitization of a nonunital Banach algebra is established, with bounds ( 1 1 and 6 exp ⁡ ( 1 ) 6\exp (1) ) uniform over the class of such algebras. A tighter bound, 3 3 , is obtained in C ∗ {C^{\ast }} -algebras for elements with Hermitian nonunital parts.