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dc.contributor.author | Bikchentaev A. | |
dc.contributor.author | Sabirova A. | |
dc.date.accessioned | 2018-09-18T20:31:40Z | |
dc.date.available | 2018-09-18T20:31:40Z | |
dc.date.issued | 2012 | |
dc.identifier.issn | 0037-4466 | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/140802 | |
dc.description.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 L 1(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 L p(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. © 2012 Pleiades Publishing, Ltd. | |
dc.relation.ispartofseries | Siberian Mathematical Journal | |
dc.subject | arithmetic average | |
dc.subject | Banach space | |
dc.subject | Banach-Saks property | |
dc.subject | Hilbert space | |
dc.subject | measurable operator | |
dc.subject | normal semifinite trace | |
dc.subject | spectral theorem | |
dc.subject | topology of convergence in measure | |
dc.subject | von Neumann algebra | |
dc.title | Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators | |
dc.type | Article | |
dc.relation.ispartofseries-issue | 2 | |
dc.relation.ispartofseries-volume | 53 | |
dc.collection | Публикации сотрудников КФУ | |
dc.relation.startpage | 207 | |
dc.source.id | SCOPUS00374466-2012-53-2-SID84860359795 |