The Boundedness Below of 2 × 2 Upper Triangular Linear Relation Matrices

Ran Huo ¹Yanyan Du ²Junjie Huang³

扫码查看

作者信息

1. School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China;College of Science,Inner Mongolia Agricultural University,Hohhot 010018,China
2. School of Mathematics and Statistics,Shandong University of Technology,Zibo 255091,China
3. School of Mathematical Sciences,Inner Mongolia University,Hohhot 010021,China
折叠

Abstract

In this note,the boundedness below of linear relation matrix MC=(A0CB)∈LR(H⊕K)is considered,where A ∈ CLR(H),B ∈ CLR(K),C ∈ BLR(K,H),H,K are separable Hilbert spaces.By suitable space decompositions,a necessary and sufficient condition for diagonal relations A,B is given so that MC is bounded below for some C ∈ BLR(K,H).Besides,the characterization of σap(MC)and σsu(MC)are obtained,and the relationship between σap(M0)and σap(MC)is further presented.

Key words

Linear relation matrix/boundedness below/approximate point spectrum/space de-composition

引用本文复制引用

基金项目

国家自然科学基金(11961052)

Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region(NM-GIRT2317)

内蒙古自治区自然科学基金(2021MS010-06)

出版年

2024

数学研究(英文)

厦门大学教学科学学院

数学研究(英文)

影响因子：0.157

ISSN：2096-9856

参考文献量22

段落导航