JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS
Let A be an algebra. A sequence {d n} of linear mappings on A is called a higher derivation if <img border=0 width=178 height=21 src="http:/fbpe/img/proy/v29n2/img01.JPG" alt="http:/fbpe/img/proy/v29n2/img01.JPG">for each a, b ? A and each nonnegative integer n. Jewell [Pac...
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Universidad Católica del Norte, Departamento de Matemáticas
2010
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oai:scielo:S0716-091720100002000032014-08-14JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRASHejazian,ShirinMirzavaziri,MadjidOmidvar Tehrani,Elahe Derivation higher derivation automatic continuity Sakai theorem Let A be an algebra. A sequence {d n} of linear mappings on A is called a higher derivation if <img border=0 width=178 height=21 src="http:/fbpe/img/proy/v29n2/img01.JPG" alt="http:/fbpe/img/proy/v29n2/img01.JPG">for each a, b ? A and each nonnegative integer n. Jewell [Pacific J. Math. 68 (1977), 91-98], showed that a higher derivation from a Banach algebra onto a semisimple Banach algebra is continuous provided that ker(d0) ? ker(d m), for all m = 1. In this paper, under a different approach using C*-algebraic tools, we prove that each higher derivation {d n} on a C*-algebra A is automatically continuous, provided that it is normal, i. e. d0 is the identity mapping on A.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.29 n.2 20102010-08-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200003en10.4067/S0716-09172010000200003 |
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Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Derivation higher derivation automatic continuity Sakai theorem |
| spellingShingle |
Derivation higher derivation automatic continuity Sakai theorem Hejazian,Shirin Mirzavaziri,Madjid Omidvar Tehrani,Elahe JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS |
| description |
Let A be an algebra. A sequence {d n} of linear mappings on A is called a higher derivation if <img border=0 width=178 height=21 src="http:/fbpe/img/proy/v29n2/img01.JPG" alt="http:/fbpe/img/proy/v29n2/img01.JPG">for each a, b ? A and each nonnegative integer n. Jewell [Pacific J. Math. 68 (1977), 91-98], showed that a higher derivation from a Banach algebra onto a semisimple Banach algebra is continuous provided that ker(d0) ? ker(d m), for all m = 1. In this paper, under a different approach using C*-algebraic tools, we prove that each higher derivation {d n} on a C*-algebra A is automatically continuous, provided that it is normal, i. e. d0 is the identity mapping on A. |
| author |
Hejazian,Shirin Mirzavaziri,Madjid Omidvar Tehrani,Elahe |
| author_facet |
Hejazian,Shirin Mirzavaziri,Madjid Omidvar Tehrani,Elahe |
| author_sort |
Hejazian,Shirin |
| title |
JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS |
| title_short |
JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS |
| title_full |
JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS |
| title_fullStr |
JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS |
| title_full_unstemmed |
JEWELL THEOREM FOR HIGHER DERIVATIONS ON C*-ALGEBRAS |
| title_sort |
jewell theorem for higher derivations on c*-algebras |
| publisher |
Universidad Católica del Norte, Departamento de Matemáticas |
| publishDate |
2010 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172010000200003 |
| work_keys_str_mv |
AT hejazianshirin jewelltheoremforhigherderivationsoncalgebras AT mirzavazirimadjid jewelltheoremforhigherderivationsoncalgebras AT omidvartehranielahe jewelltheoremforhigherderivationsoncalgebras |
| _version_ |
1718439768907317248 |