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

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.