The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices
Cited by
Export citation
- BibTex
- RIS
- TXT
@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 = {
In this note, the boundedness below of linear relation matrix $M_{C}=\left(\begin{smallmatrix} A & C \\ 0 & B\\ \end{smallmatrix} \right)\in LR(H\oplus K)$ 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.
},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v57n1.24.04},
url = {http://global-sci.org/intro/article_detail/jms/22988.html}
}
TY - JOUR
T1 - The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices
AU - Huo , Ran
AU - Du , Yanyan
AU - Huang , Junjie
JO - Journal of Mathematical Study
VL - 1
SP - 71
EP - 83
PY - 2024
DA - 2024/03
SN - 57
DO - http://doi.org/10.4208/jms.v57n1.24.04
UR - https://global-sci.org/intro/article_detail/jms/22988.html
KW - Linear relation matrix, boundedness below, approximate point spectrum, space decomposition.
AB -
In this note, the boundedness below of linear relation matrix $M_{C}=\left(\begin{smallmatrix} A & C \\ 0 & B\\ \end{smallmatrix} \right)\in LR(H\oplus K)$ 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.
Huo , RanDu , Yanyan and Huang , Junjie. (2024). The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices.
Journal of Mathematical Study. 57 (1).
71-83.
doi:10.4208/jms.v57n1.24.04
Copy to clipboard