| Goodearl-Menal Pairs of Linear Transformations |
| Received:January 30, 2013 Revised:June 04, 2013 |
| Key Words:
Goodearl-Menal condition infinite-dimensional vector space linear transformation GM pair.
|
| Fund Project: |
|
| Hits: 2431 |
| Download times: 2055 |
| Abstract: |
| In this short note we discuss the GM property of some special linear transformation pairs over infinite-dimensional vector spaces. In particular, it is proved that if $R={\rm End}(V_D)$ is the endomorphism ring of an infinite-dimensional right vector space $V$ over a division ring $D$ with $|C(D)|>3$ and $g\in R$, then $(a_0+a_1g,\,g)$ is a GM pair for any $a_0,\,a_1\in C(D)$. Furthermore, two existing results are obtained as immediate consequences. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2014.02.005 |
| View Full Text View/Add Comment |
|
|
|
