On extensions of some nonlinear maps in vector lattices
On extensions of some nonlinear maps in vector lattices
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关于向量格中某些非线性映射的推广
DOI：
10.1016/j.jmaa.2017.05.063
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发表时间：
2017
影响因子：
1.3
通讯作者：
M. Pliev
中科院分区：
文献类型：
--
作者：
N. Abasov;M. Pliev
我们证明了定义在向量格的正规子格上的Urysohn格预同态可以扩展到整个空间，并且扩展算子是一个Urysohn格同态。引入了一类新的非线性算子φ-算子，并描述了它们的一些性质。最后，我们研究了一个由定义在向量格上的Urysohn格同态支配的正正交加性算子结构，并在Dedekind完全向量格上取值。
We show that an Urysohn lattice pre-homomorphism defined on a normal sublatticeDof a vector latticeEcan be extended to the whole spaceEand the extended operator is an Urysohn lattice homomorphism. We introduce a new class of nonlinear operators which calledφ-operators and describe some of their properties. Finally we investigate a structure of positive orthogonally additive operators dominated by an Urysohn lattice homomorphism defined on a vector latticeEand taking value in Dedekind complete vector latticeF.