Unit-free versions of the Vidav-Palmer theorem and of the Blecher-Ruan-Sinclair non-associative characterization of unital $C^*$-algebras

Abstract

We prove unit-free versions of both the associative and the non-associative Vidav-Palmer theorems. Then these results are applied to prove a unit-free version of the Blecher-Ruan-Sinclair non-associative characterization of unital $C^*$-algebras.Comment: 32 page