Algebraic isomorphisms and Jordan derivations of -subspace lattice algebras
Algebraic isomorphisms and Jordan derivations of -subspace lattice algebras
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DOI：
10.4064/sm158-3-7
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发表时间：
2003
影响因子：
0.8
通讯作者：
Fangyan Lu;Pengtong Li
中科院分区：
文献类型：
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作者：
Fangyan Lu;Pengtong Li
证明了J -子空间格代数的标准子代数之间的每一个代数同构都是拟空间的，并且J -子空间格代数的标准子代数的每一个Jordan导子都是可加导子.证明了J -子空间格代数中的每一个有限秩算子都可以表示为属于该代数的每一个秩为1的算子的有限和。作为补充，证明了J -子空间格代数到任意环上的乘法双射是自动可加的。这些结果可以应用于原子布尔子空间格代数和五边形子空间格代数。
It is shown that every algebraic isomorphism between standard subalgebras of J -subspace lattice algebras is quasi-spatial and every Jordan derivation of standard subalgebras of J -subspace lattice algebras is an additive derivation. Also, it is proved that every finite rank operator in a J -subspace lattice algebra can be written as a finite sum of rank one operators each belonging to that algebra. As an additional result, a multiplicative bijection of a J -subspace lattice algebra onto an arbitrary ring is proved to be automatically additive. Those results can be applied to atomic Boolean subspace lattice algebras and pentagon subspace lattice algebras.