International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 2, Pages 317-322
doi:10.1155/S0161171295000408
An application of the Sakai's theorem to the characterization of H*-algebras
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.
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.