论文标题
不对称规范空间的对称和拓扑分类索引
Index of symmetry and topological classification of asymmetric normed spaces
论文作者
论文摘要
令x，y为不对称的范围空间，LC（x，y）从x到y的所有线性连续运算符的凸锥。众所周知，LC（x，y）不是矢量空间。本说明的目的是使用Baire类别定理证明，如果LC（X，Y）是某些不对称范数Y的矢量空间，则X与其相关的规范空间是同构的（对于每个非对称范围的空间y都是正确的，并且易于建立）。为此，我们介绍了$ [0，1]的太空x的对称索引，我们给出了索引C（x）与LC（x，y）之间的链接，而LC（x，y）则是每个不对称的规范空间的不对称规范空间。我们的研究导致我们的拓扑范围分类，导致了不对称的规范性的拓扑。
Let X, Y be asymmetric normed spaces and Lc(X, Y) the convex cone of all linear continuous operators from X to Y. It is known that in general, Lc(X, Y) is not a vector space. The aim of this note is to prove, using the Baire category theorem, that if Lc(X, Y) is a vector space for some asymmetric normed space Y , then X is isomorphic to its associated normed space (the converse is true for every asymmetric normed space Y and is easy to establish). For this, we introduce an index of symmetry of the space X denoted c(X) $\in$ [0, 1] and we give the link between the index c(X) and the fact that Lc(X, Y) is in turn an asymmetric normed space for every asymmetric normed space Y. Our study leads to a topological classification of asymmetric normed spaces.
