Semi-simplicity of a proper weak H*-algebra

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...

Full description

Saved in:
Bibliographic Details
Main Author: Parfeny P. Saworotnow
Format: Article
Language:English
Published: Wiley 1992-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Subjects:
Online Access:http://dx.doi.org/10.1155/S0161171292000541
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849399886278033408
author Parfeny P. Saworotnow
author_facet Parfeny P. Saworotnow
author_sort Parfeny P. Saworotnow
collection DOAJ
description 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.
format Article
id doaj-art-a4fbf1f5e3e346798b14cfa16e6de566
institution Kabale University
issn 0161-1712
1687-0425
language English
publishDate 1992-01-01
publisher Wiley
record_format Article
series International Journal of Mathematics and Mathematical Sciences
spelling doaj-art-a4fbf1f5e3e346798b14cfa16e6de5662025-08-20T03:38:13ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251992-01-0115240941110.1155/S0161171292000541Semi-simplicity of a proper weak H*-algebraParfeny P. Saworotnow0Department of Mathematics, The Catholic University of America, Washington, D.C. 20064, USAA 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.http://dx.doi.org/10.1155/S0161171292000541Hilbert algebraH*-algebraweak right H*-algebraweak left H*-algebracomplemented algebraright complemented algebraleft complemented algebra.
spellingShingle Parfeny P. Saworotnow
Semi-simplicity of a proper weak H*-algebra
International Journal of Mathematics and Mathematical Sciences
Hilbert algebra
H*-algebra
weak right H*-algebra
weak left H*-algebra
complemented algebra
right complemented algebra
left complemented algebra.
title Semi-simplicity of a proper weak H*-algebra
title_full Semi-simplicity of a proper weak H*-algebra
title_fullStr Semi-simplicity of a proper weak H*-algebra
title_full_unstemmed Semi-simplicity of a proper weak H*-algebra
title_short Semi-simplicity of a proper weak H*-algebra
title_sort semi simplicity of a proper weak h algebra
topic Hilbert algebra
H*-algebra
weak right H*-algebra
weak left H*-algebra
complemented algebra
right complemented algebra
left complemented algebra.
url http://dx.doi.org/10.1155/S0161171292000541
work_keys_str_mv AT parfenypsaworotnow semisimplicityofaproperweakhalgebra