ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS
The main purpose of this paper is to prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X and let A(X) C L (X) be a standard operator algebra. Suppose there exists a line...
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Universidad de La Frontera. Departamento de Matemática y Estadística.
2014
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oai:scielo:S0719-064620140001000072018-10-08ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRASŠirovnik,Nejc Prime ring semiprime ring Banach space standard operator algebra derivation Jordan derivation The main purpose of this paper is to prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X and let A(X) C L (X) be a standard operator algebra. Suppose there exists a linear mapping D : A (X) ͢ L (X) satisfying the relation 2D (An) = D (An-1) A+An-1 D (A) + D (A) An-1+ AD (An-1) for all A e A (X), where n > 2 is some fixed integer. In this case D is of the form D (A) = [A, B] for all A e A (X) and some fixed B e L (X), which means that D is a linear derivation. In particular, D is continuous.info:eu-repo/semantics/openAccessUniversidad de La Frontera. Departamento de Matemática y Estadística.Cubo (Temuco) v.16 n.1 20142014-01-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462014000100007en10.4067/S0719-06462014000100007 |
| institution |
Scielo Chile |
| collection |
Scielo Chile |
| language |
English |
| topic |
Prime ring semiprime ring Banach space standard operator algebra derivation Jordan derivation |
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Prime ring semiprime ring Banach space standard operator algebra derivation Jordan derivation Širovnik,Nejc ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS |
| description |
The main purpose of this paper is to prove the following result, which is related to a classical result of Chernoff. Let X be a real or complex Banach space, let L (X) be the algebra of all bounded linear operators on X and let A(X) C L (X) be a standard operator algebra. Suppose there exists a linear mapping D : A (X) ͢ L (X) satisfying the relation 2D (An) = D (An-1) A+An-1 D (A) + D (A) An-1+ AD (An-1) for all A e A (X), where n > 2 is some fixed integer. In this case D is of the form D (A) = [A, B] for all A e A (X) and some fixed B e L (X), which means that D is a linear derivation. In particular, D is continuous. |
| author |
Širovnik,Nejc |
| author_facet |
Širovnik,Nejc |
| author_sort |
Širovnik,Nejc |
| title |
ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS |
| title_short |
ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS |
| title_full |
ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS |
| title_fullStr |
ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS |
| title_full_unstemmed |
ON CERTAIN FUNCTIONAL EQUATION IN SEMIPRIME RINGS AND STANDARD OPERATOR ALGEBRAS |
| title_sort |
on certain functional equation in semiprime rings and standard operator algebras |
| publisher |
Universidad de La Frontera. Departamento de Matemática y Estadística. |
| publishDate |
2014 |
| url |
http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462014000100007 |
| work_keys_str_mv |
AT 352irovniknejc oncertainfunctionalequationinsemiprimeringsandstandardoperatoralgebras |
| _version_ |
1714206787485302784 |