Abstract
Let M be a type I von Neumann algebra with the center Z and let LS(M) be the algebra of all locally measurable operators affiliated with M. We prove that every Z-linear derivation on LS(M) is inner. In particular, all Z-linear derivations on the algebras of measurable and respectively totally measurable operators are spatial and implemented by elements of LS(M).
| Original language | English |
|---|---|
| Pages (from-to) | 86-94 |
| Number of pages | 9 |
| Journal | Siberian Advances in Mathematics |
| Volume | 18 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jul 2008 |
| Externally published | Yes |
Keywords
- Derivation
- Inner derivation
- Kaplansky-Hilbert module
- Locally measurable operator
- Measurable operator
- TypeI algebra
- von Neumann algebras
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