Characterization of two-sided generalized derivations
Let A be a unital semiprime, complex normed ∗-algebra and let f, g, h : A → A be linear mappings such that f and g+h are continuous. Under certain conditions, we prove that if f(p ◦ p) = g(p) ◦ p + p ◦ h(p) holds for any projection p of A, then f and g+h are two-sided generalized derivations, where...
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2020
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| Sorozat: | Acta scientiarum mathematicarum
86 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| doi: | 10.14232/actasm-020-295-8 |
| Online Access: | http://acta.bibl.u-szeged.hu/73905 |
| Tartalmi kivonat: | Let A be a unital semiprime, complex normed ∗-algebra and let f, g, h : A → A be linear mappings such that f and g+h are continuous. Under certain conditions, we prove that if f(p ◦ p) = g(p) ◦ p + p ◦ h(p) holds for any projection p of A, then f and g+h are two-sided generalized derivations, where a◦b = ab+ba. We present some consequences of this result. Moreover, we show that if A is a semiprime algebra with the unit element e and n > 1 is an integer such that the linear mappings f, g : A → A satisfy f(x n ) = Pn j=1 x n−j g(x)x j−1 for all x ∈ A and further g(e) ∈ Z(A), then f and g are two-sided generalized derivations associated with the same derivation. Also, we show that if A is a unital, semiprime Banach algebra and F, G: A → A are linear mappings satisfying F(b) = −bG(b −1 )b for all invertible elements b ∈ A, then F and G are two-sided generalized derivations. Some other related results are also discussed. |
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| Terjedelem/Fizikai jellemzők: | 577-600 |
| ISSN: | 2064-8316 |