Domination problem for narrow orthogonally additive operators
Domination problem for narrow orthogonally additive operators
复制标题
窄正交加性算子的支配问题
DOI：
10.1007/s11117-016-0401-9
复制
发表时间：
2015
期刊：
影响因子：
1
通讯作者：
M. Pliev
中科院分区：
文献类型：
--
作者：
M. Pliev
描述线性正算子片段布尔代数结构的“上下”定理是算子理论中众所周知的结果。对于定义在向量格上并在Dedekind完全向量格上取值的正抽象Uryson算子，我们证明了这个定理的一个类比。利用这一结果证明了从一个有序连续范数的向量格E到一个有序连续范数的Banach格F的有序窄正抽象Uryson算子的支配定理。
The “Up-and-down” theorem which describes the structure of the Boolean algebra of fragments of a linear positive operator is the well known result in operator theory. We prove an analog of this theorem for a positive abstract Uryson operator defined on a vector lattice and taking values in a Dedekind complete vector lattice. This result is used to prove a theorem of domination for order narrow positive abstract Uryson operators from a vector lattice E to a Banach lattice F with an order continuous norm.