Strong 3-commutativity preserving maps on standard operator algebras
| Autor: | Mei Yun Liu, Jinchuan Hou |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Acta Mathematica Sinica, English Series. 33:1659-1670 |
| ISSN: | 1439-7617 1439-8516 |
| Popis: | Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B(X). A map Φ:A→A is said to be strong 3-commutativity preserving if [Φ(A), Φ(B)]3 = [A,B]3 for all A,B ∈ A, where [A,B]3 is the 3-commutator of A,B defined by [A,B]3 = [[[A,B],B],B] with [A,B] =AB−BA. The main result in this paper is shown that, if Φ is a surjective map on A, then Φ is strong 3-commutativity preserving if and only if there exist a functional h:A→F and a scalar λ ∈ F with λ4 = 1 such that Φ(A) = λA + h(A)I for all A ∈ A. |
| Databáze: | OpenAIRE |
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