Abstract
In this article, some properties of measurable operators associated with a von Neumann algebra are considered. The concept of step operator is defined and it is proved that any positive measurable operator can be strongly approximated by some step operators on its domain, which means that any positive measurable operator can be strongly approximated by some projections on its domain. In addition, the measurability of composition operator of measurable operator and bounded operator is discussed.
| Translated title of the contribution | Properties of Measurable Operators Associated with a von Neumann Algebra |
|---|---|
| Original language | Chinese (Traditional) |
| Pages (from-to) | 293-302 |
| Number of pages | 10 |
| Journal | Acta Mathematica Sinica, Chinese Series |
| Volume | 62 |
| Issue number | 2 |
| Publication status | Published - 1 Mar 2019 |