论文标题
在刻板印象空间类别中的张量分数和张量产品上
On tensor fractions and tensor products in the category of stereotype spaces
论文作者
论文摘要
我们证明了两个身份，可以将某些天然张量产品与类别$ \ sf {lcs} $类别的类别凸空间中的一些天然张量产品连接到刻板印象空间的类别$ \ sf {ste} $中的张量产品。特别是，我们提供了足够的条件，身份$$ x^\ vartriangle \ odot y^\ vartriangle \ con（x^\ vartriangle \ cdot y^\ vartriangle）^\ vartriangle）^\ vartriangle \ cong（x \ cong（x \ con） $ \ sf {ste} $，$ \ cdot $，类别$ \ sf {lcs} $中的主要张量产品和$ \ vartriangle $，类别$ \ sf {lcs} $中的伪饱和操作。研究这种类型的关系是合理的，因为它们原来是基于信封的概念来构建二元性理论的重要工具。特别是，它们用于二元理论的构建（不一定是Abelian）可计数分组的类别。
We prove two identities that connect some natural tensor products in the category $\sf{LCS}$ of locally convex spaces with the tensor products in the category $\sf{Ste}$ of stereotype spaces. In particular, we give sufficient conditions under which the identity $$ X^\vartriangle\odot Y^\vartriangle\cong (X^\vartriangle\cdot Y^\vartriangle)^\vartriangle\cong (X\cdot Y)^\vartriangle $$ holds, where $\odot$ is the injective tensor product in the category $\sf{Ste}$, $\cdot$, the primary tensor product in the category $\sf{LCS}$, and $\vartriangle$, the pseudosaturation operation in the category $\sf{LCS}$. Studying the relations of this type is justified by the fact that they turn out to be important instruments for constructing duality theory based on the notion of envelope. In particular, they are used in the construction of the duality theory for the class of (not necessarily, Abelian) countable discrete groups.
