论文标题
向量晶格的限制
Limits of vector lattices
论文作者
论文摘要
如果$ k $是一个紧凑的Hausdorff空间，那么Banach晶格$ c（k）$是等同于晶格同构与某些Banach晶格的双重同构，则可以将$ c（k）$分解为$ \ ell^\ ell^\ ell^\ ell^\ elfty $ direct $ -Direct-direct of Maximal Singular Singular Singular of Cross contress $ contress $ contornal $ c的运营商（K）为了将此结果概括为contecter lattice $ c（x）$在realmpact space $ x $上连续的，实际有价值的功能，我们考虑在适当类别的矢量晶格类别中的直接和反向限制。我们开发了针对此类限制的双重性理论，并应用该理论表明$ c（x）$在某些矢量晶格$ f $ f $ f $ f $ f $ f $ i时及时只有$ c（x）$可以分解为$ c（x）$ c（x）$的所有订单连续功能的逆极限时。实际上，我们获得了一个更一般的结果：当且仅当它是晶格同构与$ e $上适当的订单连续功能家族的载体的逆极限时，Dedekind完整的矢量晶格$ e $是完美的。提出了许多其他应用程序，包括根据ra量量度的空间进行订单双空间的分解定理。
If $K$ is a compact Hausdorff space so that the Banach lattice $C(K)$ is isometrically lattice isomorphic to a dual of some Banach lattice, then $C(K)$ can be decomposed as the $\ell^\infty$-direct sum of the carriers of a maximal singular family of order continuous functionals on $C(K)$. In order to generalise this result to the vector lattice $C(X)$ of continuous, real valued functions on a realcompact space $X$, we consider direct and inverse limits in suitable categories of vector lattices. We develop a duality theory for such limits and apply this theory to show that $C(X)$ is lattice isomorphic to the order dual of some vector lattice $F$ if and only if $C(X)$ can be decomposed as the inverse limit of the carriers of all order continuous functionals on $C(X)$. In fact, we obtain a more general result: A Dedekind complete vector lattice $E$ is perfect if and only if it is lattice isomorphic to the inverse limit of the carriers of a suitable family of order continuous functionals on $E$. A number of other applications are presented, including a decomposition theorem for order dual spaces in terms of spaces of Radon measures.
