Narrow orthogonally additive operators in lattice-normed spaces
Narrow orthogonally additive operators in lattice-normed spaces
复制标题
格范空间中的窄正交加性算子
DOI：
10.1134/s0037446617010177
复制
发表时间：
2015
影响因子：
0.5
通讯作者：
X. Fang
中科院分区：
文献类型：
--
作者：
M. Pliev;X. Fang
考虑了格赋范空间中一类新的窄正交可加算子，证明了从Banach-Kantorovich空间V到Banach空间Y的每一个C-紧范数横向连续正交可加算子的窄性.此外，从V到Banach序列格Y的每个控制Urysohn算子也是狭义的.我们证明了从Banach-Kantorovich空间V到具有混合范数W的Banach空间的控制Urysohn算子的序窄性蕴涵了该算子的最小控制算子的序窄性.
We consider a new class of narrow orthogonally additive operators in lattice-normed spaces and prove the narrowness of every C-compact norm-laterally-continuous orthogonally additive operator from a Banach–Kantorovich space V into a Banach space Y. Furthermore, every dominated Urysohn operator from V into a Banach sequence lattice Y is also narrow. We establish that the order narrowness of a dominated Urysohn operator from a Banach–Kantorovich space V into a Banach space with mixed norm W implies the order narrowness of the least dominant of the operator.