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 |
|