Narrow orthogonally additive operators
Narrow orthogonally additive operators
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窄正交加法算子
DOI：
10.1007/s11117-013-0268-y
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发表时间：
2013
期刊：
影响因子：
1
通讯作者：
M. Popov
中科院分区：
文献类型：
--
作者：
M. Pliev;M. Popov
我们将狭义算子的概念推广到向量格上的非线性映射。主要对象是正交加法算子，特别是抽象的Uryson算子。大部分结果推广了O. Maslyuchenko，V. Mykhaylyuk和第二位作者发表在Positivity 13：459-495（2009）中，用于线性算子。例如，我们证明了从无原子的Dedekind完备向量格到Banach空间的每一个正交可加的侧范数连续C-紧算子都是窄的。另一个结果是所有阶窄横向连续抽象Uryson算子的集合U_{on}^{lc}（E，F）Uonlc（E，F）是从具有主投影性质的无原子向量格E到Dedekind完备向量格F的所有横向连续抽象Uryson算子的向量格中的一个带.由保持不交性的横向连续抽象Uryson算子生成的带是$${\mathcal U}_n^{lc}（E，F）$$Unlc（E，F）的正交补。
We generalize the notion of narrow operators to nonlinear maps on vector lattices. The main objects are orthogonally additive operators and, in particular, abstract Uryson operators. Most of the results extend known theorems obtained by O. Maslyuchenko, V. Mykhaylyuk and the second named author published in Positivity 13:459–495 (2009) for linear operators. For instance, we prove that every orthogonally additive laterally-to-norm continuous C-compact operator from an atomless Dedekind complete vector lattice to a Banach space is narrow. Another result asserts that the set $${\mathcal U}_{on}^{lc}(E,F)$$Uonlc(E,F) of all order narrow laterally continuous abstract Uryson operators is a band in the vector lattice of all laterally continuous abstract Uryson operators from an atomless vector lattice $$E$$E with the principal projection property to a Dedekind complete vector lattice $$F$$F. The band generated by the disjointness preserving laterally continuous abstract Uryson operators is the orthogonal complement to $${\mathcal U}_n^{lc}(E,F)$$Unlc(E,F).