On some functional equations on standard operator algebras /
The main purpose of this paper is to prove the following result. Let ▫$X$▫ be a real or complex Banach space, let ▫$L(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫, let ▫$A(X) \subseteq L(X)$▫ be a standard operator algebra, and let ▫$T : A(X) \to L(X($▫ be an additive mapping satisfy...
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| Main Authors: | , |
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| Format: | Book Chapter |
| Jezik: | English |
| Teme: | |
| Sorodne knjige/članki: | Vsebovano v:
Glasnik matematički. Serija 3 |
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| Izvleček: | The main purpose of this paper is to prove the following result. Let ▫$X$▫ be a real or complex Banach space, let ▫$L(X)$▫ be the algebra of all bounded linear operators on ▫$X$▫, let ▫$A(X) \subseteq L(X)$▫ be a standard operator algebra, and let ▫$T : A(X) \to L(X($▫ be an additive mapping satisfying the relation ▫$T(A^{2n+1}) = \sum_{i=1}^{2n+1}(-1)^{i+1} A^{i-1} T(A) A^{2n+1-i}$▫, for all ▫$A \in A(X)$▫ and some fixed integer ▫$n \ge 1$▫. In this case ▫$T$▫ is of the form ▫$T(A) = AB + BA$▫, for all ▫$A \in A(X)$▫ and some fixed ▫$B \in L(X)$▫. In particular, ▫$T$▫ is continuous. |
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| Fizični opis: | str. 447-455. |
| Bibliografija: | Bibliografija: str. 454-455. Abstract. |
| ISSN: | 0017-095X |