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...
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| Format: | Article |
| Language: | English |
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Wiley
1992-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171292000541 |
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| _version_ | 1849399886278033408 |
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| 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 |