An application of the Sakai's theorem to the characterization of H*-algebras

Abstract

The well-known Sakai's theorem, which states that every derivation acting on a von Neumann algebra is inner, is ,used to obtain a new elegant proof of the Saworotnow's characterization theorem for associative H*-algebras via two-sided H*-algebras. This proof completely avoids structure theory.

Keywords

• H*-algebra
• involution
• automorphism
• derivation
• centralizer
• von Neumann algebra.