Riesz* homomorphisms on pre-Riesz spaces consisting of continuous functions
Riesz* homomorphisms on pre-Riesz spaces consisting of continuous functions
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由连续函数组成的前 Riesz 空间上的 Riesz* 同态
DOI：
10.1007/s11117-017-0519-4
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发表时间：
2018
期刊：
影响因子：
1
通讯作者：
H. V. Imhoff
中科院分区：
文献类型：
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作者：
H. V. Imhoff
在Riesz空间（向量格）上的算子理论中，一个重要的结果是C（X）上的Riesz同态（格同态）恰是加权复合算子。我们将这个结果推广到C（X）的序稠密子空间上的Riesz* 同态。在这些子空间上，我们考虑和比较各类运营商的Riesz同态的概念扩展。进一步，利用Riesz* 同态的加权复合结构，得到了关于双射Riesz* 同态的几个结果.特别地，我们刻画了C（X）的序稠密子空间的自同构群。最后，我们对局部紧Hausdorff空间X，在$$C_0（X）$C_0（X）的子空间上建立了Riesz* 同态的类似理论，并将其应用于光滑流形和Sobolev空间。
In the theory of operators on a Riesz space (vector lattice), an important result states that the Riesz homomorphisms (lattice homomorphisms) on C(X) are exactly the weighted composition operators. We extend this result to Riesz* homomorphisms on order dense subspaces of C(X). On those subspace we consider and compare various classes of operators that extend the notion of a Riesz homomorphism. Furthermore, using the weighted composition structure of Riesz* homomorphisms we obtain several results concerning bijective Riesz* homomorphisms. In particular, we characterize the automorphism group for order dense subspaces of C(X). Lastly, we develop a similar theory for Riesz* homomorphisms on subspace of $$C_0(X)$$C0(X), for a locally compact Hausdorff space X, and apply it to smooth manifolds and Sobolev spaces.