HERMITIANS IN MATRIX ALGEBRAS WITH OPERATOR NORM

We investigate the real space H of Hermitian matrices in M-n(C) with respect to norms on C-n. For absolute norms, the general form of Hermitian matrices was essentially established by Schneider and Turner [Schneider and Turner, Linear and Multilinear Algebra (1973), 9-31]. Here, we offer a much shorter proof. For non-absolute norms, we begin an investigation of H by means of a series of examples, with particular reference to dimension and commutativity.