An extreme point theorem for inverses in a Banach algebra with identity

Abstract

A version of Corollary 2 for Hilbert space was orally communicated to the author by C. Pearcy. His proof employed facts about the numerical range, inner products, and orthogonality, and thus made use of structure peculiar to Hilbert space. A Banach algebra with identity is a more comfortable setting for these results, and there it is much clearer just what is important in each proof.