Abstract
Akcoglu and Suchaston proved the following result: Let T : L 1(X,F,μ) → L1(X, F, μ) be a positive contraction. Assume that for z ∈ L1(X,F,μ) the sequence (Tnz) converges weakly in L1(X,F,μ). Then either limn→∞ ∥Tnz∥ = 0 or there exists a positive function h ∈ L1(X, F,μ),h ≠ 0 such that Th = h. In the paper we prove an extension of this result in a finite von Neumann algebra setting, and as a consequence we obtain that if a positive contraction of a noncommutative L1-space has no nonzero positive invariant element, then its mixing property implies the completely mixing property.
Original language | English |
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Pages (from-to) | 843-850 |
Number of pages | 8 |
Journal | Proceedings of the American Mathematical Society |
Volume | 134 |
Issue number | 3 |
DOIs | |
Publication status | Published - Mar 2006 |
Externally published | Yes |
Keywords
- Completely mixing
- Mixing
- Non Neumann algebra
- Positive contraction
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics