On mixing and completely mixing properties of positive L 1-contractions of finite von Neumann algebras

Farruh Mukhamedov, Seyit Temir, Hasan Akin

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)843-850
Number of pages8
JournalProceedings of the American Mathematical Society
Volume134
Issue number3
DOIs
Publication statusPublished - Mar 2006
Externally publishedYes

Keywords

  • Completely mixing
  • Mixing
  • Non Neumann algebra
  • Positive contraction

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On mixing and completely mixing properties of positive L 1-contractions of finite von Neumann algebras'. Together they form a unique fingerprint.

Cite this