dc.contributor.author |
Bikchentaev A. |
|
dc.date.accessioned |
2018-09-17T21:58:46Z |
|
dc.date.available |
2018-09-17T21:58:46Z |
|
dc.date.issued |
2004 |
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dc.identifier.issn |
1995-0802 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/135676 |
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dc.description.abstract |
Let M be a semifinite von Neumann algebra in a Hilbert space H and τ be a normal faithful semifinite trace on M. Let Mpr denote the set of all projections in M, e denote the unit of M, and ∥ · ∥ denote the C*-norm on M. The set of all τ-measurable operators M̃ with sum and product defined as the respective closures of the usual sum and product, is a *-algebra. The sets U(ε, δ)={x ε M̃: ∥xpk∥ ≤ ε and τ (e - p) ≤ δ for some p ε Mpr} ε>0; δ>0; form a base at 0 for a metrizable vector topology tτ on M̃, called the measure topology. Equipped with this topology, M̃ is a complete topological *-algebra. We will write xi τ→ x in case a net {xi} iεI ⊂ M̃ converges to x ε M̃ for the measure topology on M̃. By definition, a net {xi}iεI ⊂ M̃ converges τ-locally to x ε M̃ (notation: x i τl→ x) if xip τ→ xp for all p ε Mpr, τ(p) < ∞; and a net {xi} iεI ⊂ M̃ converges weak τ-locally to x ε M̃ (notation: xi wτl→ x) if xip τ→ pxp for all p ε Mpr, τ(p) < ∞. |
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dc.relation.ispartofseries |
Lobachevskii Journal of Mathematics |
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dc.subject |
Compact operator |
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dc.subject |
Convergence with respect to measure |
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dc.subject |
Hilbert space |
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dc.subject |
Measurable operator |
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dc.subject |
Noncommutative integration |
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dc.subject |
Semifinite trace |
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dc.subject |
Topological algebra |
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dc.subject |
Von Neumann algebra |
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dc.title |
The continuity of multiplication for two topologies associated with a semifinite trace on von neumann algebra |
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dc.type |
Article |
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dc.relation.ispartofseries-volume |
14 |
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dc.collection |
Публикации сотрудников КФУ |
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dc.relation.startpage |
17 |
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dc.source.id |
SCOPUS19950802-2004-14-SID4444237151 |
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