论文标题
极化身份
Polarization Identities
论文作者
论文摘要
我们证明了线性代数的极化认同的概括，该线性代数以规范表示复杂的内部产物空间的内部产物，在这种情况下，标量领域扩展到具有差异的关联代数，而极化被视为标量的压实乘法超级分级，将极化视为平均化操作。使用此情况，我们证明了Jordan-Von Neumann定理的一般形式，即当在关联代数中采用标量时，在规范线性空间之间表征内部产物空间。
We prove a generalization of the polarization identity of linear algebra expressing the inner product of a complex inner product space in terms of the norm, where the field of scalars is extended to an associative algebra equipped with an involution, and polarization is viewed as an averaging operation over a compact multiplicative subgroup of the scalars. Using this we prove a general form of the Jordan-von Neumann theorem on characterizing inner product spaces among normed linear spaces, when the scalars are taken in an associative algebra.
