dc.contributor.author |
Novikov A. |
|
dc.date.accessioned |
2018-09-19T21:15:04Z |
|
dc.date.available |
2018-09-19T21:15:04Z |
|
dc.date.issued |
2016 |
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dc.identifier.issn |
1385-1292 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/143680 |
|
dc.description.abstract |
© 2016 Springer International PublishingIn this paper we suggest an approach for constructing an (Formula presented.)-type space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we introduce a seminorm, and prove that it is a norm if and only if the operator is injective. For this norm we construct an (Formula presented.)-type space as the complition of the space of hermitian ultraweakly continuous linear functionals on von Neumann algebra, and represent (Formula presented.)-type space as a space of continuous linear functionals on the space of special sesquilinear forms. Also, we prove that (Formula presented.)-type space is isometrically isomorphic to the predual of von Neumann algebra in a natural way. We give a small list of alternate definitions of the seminorm, and a special definition for the case of semifinite von Neumann algebra, in particular. We study order properties of (Formula presented.)-type space, and demonstrate the connection between semifinite normal weights and positive elements of this space. At last, we construct a similar L-space for the positive element of C*-algebra, and study the connection between this L-space and the (Formula presented.)-type space in case when this C*-algebra is a von Neumann algebra. |
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dc.relation.ispartofseries |
Positivity |
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dc.subject |
$$L_1$$L1-space |
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dc.subject |
C*-algebra |
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dc.subject |
Noncommutative integration |
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dc.subject |
Operator algebra |
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dc.subject |
Positive operator |
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dc.subject |
Semifinite normal weight |
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dc.subject |
Unbounded operator |
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dc.subject |
Von Neumann algebra |
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dc.title |
L1-space for a positive operator affiliated with von Neumann algebra |
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dc.type |
Article in Press |
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dc.collection |
Публикации сотрудников КФУ |
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dc.relation.startpage |
1 |
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dc.source.id |
SCOPUS13851292-2016-SID84969791877 |
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