Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras
Let ๐ด, ๐ต be two unital ๐ถโ-algebras. We prove that every almost unital almost linear mapping โ : ๐ดโ๐ต which satisfies โ(3๐๐ข๐ฆ+3๐๐ฆ๐ข)=โ(3๐๐ข)โ(๐ฆ)+โ(๐ฆ)โ(3๐๐ข) for all ๐ขโ๐(๐ด), all ๐ฆโ๐ด, and all ๐=0,1,2,โฆ, is a Jordan homomorphism. Also, for a unital ๐ถโ-algebra ๐ด of real rank zero, every almost unital almost l...
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2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/513128 |
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| author | A. Ebadian S. Kaboli Gharetapeh M. Eshaghi Gordji |
| author_facet | A. Ebadian S. Kaboli Gharetapeh M. Eshaghi Gordji |
| author_sort | A. Ebadian |
| collection | DOAJ |
| description | Let ๐ด, ๐ต be two unital ๐ถโ-algebras. We prove that every almost unital almost
linear mapping โ : ๐ดโ๐ต which satisfies โ(3๐๐ข๐ฆ+3๐๐ฆ๐ข)=โ(3๐๐ข)โ(๐ฆ)+โ(๐ฆ)โ(3๐๐ข) for all ๐ขโ๐(๐ด), all ๐ฆโ๐ด, and all ๐=0,1,2,โฆ, is a Jordan homomorphism. Also, for a unital
๐ถโ-algebra ๐ด of real rank zero, every almost unital almost linear continuous mapping โโถ๐ดโ๐ต is a Jordan homomorphism when โ(3๐๐ข๐ฆ+3๐๐ฆ๐ข)=โ(3๐๐ข)โ(๐ฆ)+โ(๐ฆ)โ(3๐๐ข)
holds
for all ๐ขโ๐ผ1
(๐ดsa), all ๐ฆโ๐ด, and all ๐=0,1,2,โฆ. Furthermore, we investigate the Hyers-
Ulam-Aoki-Rassias stability of Jordan โ-homomorphisms between unital ๐ถโ-algebras by using the fixed points methods. |
| format | Article |
| id | doaj-art-de4c2da2815c43e89b898a05e380aa57 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-de4c2da2815c43e89b898a05e380aa572025-02-03T01:09:25ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/513128513128Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-AlgebrasA. Ebadian0S. Kaboli Gharetapeh1M. Eshaghi Gordji2Department of Mathematics, Urmia University, Urmia, IranDepartment of Mathematics, Urmia University, Urmia, IranDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranLet ๐ด, ๐ต be two unital ๐ถโ-algebras. We prove that every almost unital almost linear mapping โ : ๐ดโ๐ต which satisfies โ(3๐๐ข๐ฆ+3๐๐ฆ๐ข)=โ(3๐๐ข)โ(๐ฆ)+โ(๐ฆ)โ(3๐๐ข) for all ๐ขโ๐(๐ด), all ๐ฆโ๐ด, and all ๐=0,1,2,โฆ, is a Jordan homomorphism. Also, for a unital ๐ถโ-algebra ๐ด of real rank zero, every almost unital almost linear continuous mapping โโถ๐ดโ๐ต is a Jordan homomorphism when โ(3๐๐ข๐ฆ+3๐๐ฆ๐ข)=โ(3๐๐ข)โ(๐ฆ)+โ(๐ฆ)โ(3๐๐ข) holds for all ๐ขโ๐ผ1 (๐ดsa), all ๐ฆโ๐ด, and all ๐=0,1,2,โฆ. Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan โ-homomorphisms between unital ๐ถโ-algebras by using the fixed points methods.http://dx.doi.org/10.1155/2011/513128 |
| spellingShingle | A. Ebadian S. Kaboli Gharetapeh M. Eshaghi Gordji Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras Abstract and Applied Analysis |
| title | Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras |
| title_full | Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras |
| title_fullStr | Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras |
| title_full_unstemmed | Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras |
| title_short | Nearly Jordan โ-Homomorphisms between Unital ๐ถโ-Algebras |
| title_sort | nearly jordan โ homomorphisms between unital ๐ถโ algebras |
| url | http://dx.doi.org/10.1155/2011/513128 |
| work_keys_str_mv | AT aebadian nearlyjordanhomomorphismsbetweenunitalcalgebras AT skaboligharetapeh nearlyjordanhomomorphismsbetweenunitalcalgebras AT meshaghigordji nearlyjordanhomomorphismsbetweenunitalcalgebras |