The adjoint of a bilinear operation
The adjoint of a bilinear operation
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双线性运算的伴随
DOI：
10.1090/s0002-9939-1951-0045941-1
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发表时间：
1951
期刊：
影响因子：
--
通讯作者：
R. Arens
中科院分区：
文献类型：
--
作者：
R. Arens
是m的扩展。回想一下，X，Y，Z自然地可嵌入到X-，Y--，Z-resp中。此外，某些属性，如结合性，当m具有它们时，会传递给m*（这只有在Y=Z=X时才有意义）。另一方面，交换性的传递（当Y=X时是有意义的）是开放的，并且将在本文中考虑。这个交换性问题可以概括如下。如果m满足1.1-1.3，则可以定义转置运算
is an extension of m. Recall that X, Y, Z are naturally embeddable in X-, Y--, Z-resp. Moreover, certain properties, such as associativity, when m has them, are transmitted to m*** (this makes sense only when Y=Z=X). On the other hand, the transmission of commutativity (which makes sense when Y=X) was left open, and will be considered in this paper. This question of commutativity can be generalized as follows. If m satisfies 1.1-1.3, one can define the transposed operation