@Article{JMS-57-71,
author = {Huo , RanDu , Yanyan and Huang , Junjie},
title = {The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices},
journal = {Journal of Mathematical Study},
year = {2024},
volume = {57},
number = {1},
pages = {71--83},
abstract = {<div style="text-align: justify;">In this note, the boundedness below of linear relation matrix $M_{C}=\left(\begin{smallmatrix}&nbsp; A &amp; C \\&nbsp; 0 &amp; B\\&nbsp; \end{smallmatrix} \right)\in LR(H\oplus K)$ is considered, where $A\in CLR(H)$, $B\in CLR(K),$ $C\in BLR(K,H)$, $H,K$ are separable Hilbert spaces. By suitable space decompositions, a necessary and sufficient condition for diagonal relations $A,B$ is given so that $M_{C}$ is bounded below for some $C\in BLR(K,H)$. Besides, the characterization of $\sigma_{ap}(M_{C})$ and $\sigma_{su}(M_{C})$ are obtained, and the relationship between $\sigma_{ap}(M_{0})$ and $\sigma_{ap}(M_{C})$ is further presented.</div>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v57n1.24.04},
url = {http://global-sci.org/intro/article_detail/jms/22988.html}
}