论文标题
$ bv（σ）$空间的同构
Isomorphisms of $BV(σ)$ spaces
论文作者
论文摘要
在本文中，我们调查了紧凑型集合$σ\ subseteq \ mathbb {c} $的属性与空间$ bv（σ）$的结构（在Ashton和Doust的意义上）定义为$σ$。对于$σ$上绝对连续功能的子代理，众所周知，对于某些类别的紧凑型组，一个人获得了gelfand-kolmogorov类型的结果：功能空间$ ac（σ_1）$（σ_2）$和$ ac（σ_2）$是Isomorphic，仅在域名$σ_1$ $σ_1$和$σ__2$ ne Home is Homes $ ne Homes $ ne Home。我们的主要定理是，在这种情况下，同构必须扩展到$ bv（σ）$空间的同构。 $ ac（σ）$运算符的光谱理论给出了应用。
In this paper we investigate the relationship between the properties of a compact set $σ\subseteq \mathbb{C}$ and the structure of the space $BV(σ)$ of functions of bounded variation (in the sense of Ashton and Doust) defined on $σ$. For the subalgebras of absolutely continuous functions on $σ$, it is known that for certain classes of compact sets one obtains a Gelfand--Kolmogorov type result: the function spaces $AC(σ_1)$ and $AC(σ_2)$ are isomorphic if and only if the domain sets $σ_1$ and $σ_2$ are homeomorphic. Our main theorem is that in this case the isomorphism must extend to an isomorphism of the $BV(σ)$ spaces. An application is given to the spectral theory of $AC(σ)$ operators.
