Linear Mappings Characterized by Action on Zero Products or Unit Products
Linear Mappings Characterized by Action on Zero Products or Unit Products
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DOI：
10.1007/s41980-020-00499-y
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发表时间：
2021-04
影响因子：
0.7
通讯作者：
Jiankui Li;Shan Li
中科院分区：
文献类型：
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作者：
Jiankui Li;Shan Li
设是一个单位代数，是一个单位双模。本文刻划了线性映射和从到，满足当包含分离理想时，它在由中的所有幂等元生成的代数中。我们把这个结果应用到-子空间格代数、完全分配交换子空间格代数和有单位元的标准算子代数。进一步，假设是单位Banach代数，是单位Banach双模，我们给出了线性映射的完整刻画，从m到m，对所有条件都满足。
Letbe a unital algebra andbe a unital-bimodule. We characterize the linear mappingsandfrominto, satisfyingfor everywithwhencontains a separating idealof, which is in the algebra generated by all idempotents in. We apply the result to-subspace lattice algebras, completely distributive commutative subspace lattice algebras, and unital standard operator algebras. Furthermore, suppose thatis a unital Banach algebra andis a unital Banach-bimodule, we give a complete description of linear mappingsandfrominto, satisfyingfor everywith.