Closed linear relations and their regular points
Closed linear relations and their regular points
复制标题
闭合线性关系及其正则点
DOI：
--
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
H. Winkler
中科院分区：
文献类型：
--
作者：
J. Labrousse;A. Sandovici;H. S. V. D. Sno;H. Winkler
对于希尔伯特空间 h 中的闭合线性关系 A，解析集和规则类型点集的概念被扩展到规则点集。这些点是根据 0 度的准 Fredholm 关系来定义的。规则点的集合是开集，并且由于 lambda 是该集合中 C 的元素，因此空间 ker (A - lambda) 和 ran(A - lambda) 在间隙度量中是连续的。根据相应零空间之间的间隙度量以及线性关系 A 的广义解，给出了规则点的几个特征。
For a closed linear relation A in a Hilbert space h the notions of resolvent set and set of points of regular type are extended to the set of regular points. Such points are defined in terms of quasi-Fredholm relations of degree 0. The set of regular points is open and for lambda is an element of C in this set the spaces ker (A - lambda) and ran(A - lambda) are continuous in the gap metric. Several characterizations of regular points are presented, in terms of the gap metric between corresponding null spaces, and in terms of generalized resolvents of the linear relation A.