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Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bikchentaev, Airat Midkhatovich Sabirova, A. A. |
| Copyright Year | 2012 |
| Abstract | Consider a von Neumann algebra M with a faithful normal semifinite trace τ. We prove that each order bounded sequence of τ-compact operators includes a subsequence whose arithmetic averages converge in τ. We also prove a noncommutative analog of Pratt’s lemma for L1(M, τ). The results are new even for the algebra M = B(H) of bounded linear operators with the canonical trace τ = tr on a Hilbert space H. We apply the main result to Lp(M, τ) with 0 < p ≤ 1 and present some examples that show the necessity of passing to the arithmetic averages as well as the necessity of τ-compactness of the dominant. |
| Starting Page | 207 |
| Ending Page | 216 |
| Page Count | 10 |
| File Format | PDF HTM / HTML |
| DOI | 10.1134/S0037446612020036 |
| Volume Number | 53 |
| Alternate Webpage(s) | https://shelly.kpfu.ru/e-ksu/docs/F_1444645580/0207.pdf |
| Alternate Webpage(s) | https://doi.org/10.1134/S0037446612020036 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
