Strong 2-Jordan product preserving maps on operator algebras
Strong 2-Jordan product preserving maps on operator algebras
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DOI：
10.12988/imf.2018.8845
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发表时间：
2018
影响因子：
6.1
通讯作者：
Miaomiao Wang;X. Qi
中科院分区：
文献类型：
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作者：
Miaomiao Wang;X. Qi
令R 为具有单元1 和幂等元素e1 的环。假设 f : R → R 是满射映射。结果表明，在某些温和条件下，对于所有 a ε R 和 e ε {e1, 1−e1, 1}，f 满足 {f(a), f(e)}2 = {a, e}2 当且仅当 f(1) 位于 R 的中心且 f(1)3 = 1 且 f(a) = f(1)a 对于所有 a ε R 成立。作为应用，此类映射在素环、标准算子代数和 von 上分别表征了诺依曼代数。数学学科分类：16W10； 47B49
LetR be a ring having unit 1 and an idempotent element e1. Assume that f : R → R is a surjective map. It is shown that, under some mild conditions, f satisfies {f(a), f(e)}2 = {a, e}2 for all a ∈ R and e ∈ {e1, 1−e1, 1} if and only if f(1) is in the center of R with f(1)3 = 1 and f(a) = f(1)a holds for all a ∈ R. As applications, such maps on prime rings, standard operator algebras and von Neumann algebras are characterized, respectively. Mathematics Subject Classification: 16W10; 47B49