International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 2, Pages 409-411
doi:10.1155/S0161171292000541
Semi-simplicity of a proper weak H*-algebra
Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USA
Received 23 January 1991
Copyright © 1992 Parfeny P. Saworotnow. 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
A weak right H*-algebra is a Banach algebra A which is a Hilbert space and which has a dense subset Dr with the property that for each x in Dr there exists xr such that (yx,z)=(y,zxr) for all y, z in A. It is shown that a proper (each xr is unique) weak right H*-algebra is semi-simple. Also there is an example of weak right H*-algebra which is not a left H*-algebra.