International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 317-322

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

Borut Zalar

University of Ljubljana, Institute of Mathematics, Jadranska 19, Ljubljana 61000, Slovenia

Received 11 May 1993

Copyright © 1995 Borut Zalar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.