Abstract
Given a von Neumann algebra M we consider its central extension E(M). For type I von Neumann algebras, E(M) coincides with the algebra LS(M) of all locally measurable operators affiliated with M: In this case we show that an arbitrary automorphism T of E(M) can be decomposed as T = Ta ο Tφ where Ta(x) = axa-1 is an inner automorphism implemented by an element a 2 ∈ (M), and T φ is a special automorphism generated by an automorphism φ of the center of E(M): In particular if M is of type I∞ then every band preserving automorphism of E(M) is inner.
| Original language | English |
|---|---|
| Pages (from-to) | 1-17 |
| Number of pages | 17 |
| Journal | Studia Mathematica |
| Volume | 207 |
| Issue number | 1 |
| DOIs | |
| State | Published - 2011 |
| Externally published | Yes |
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