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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 | |
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. | |
dc.relation.ispartofseries | Positivity | |
dc.subject | $$L_1$$L1-space | |
dc.subject | C*-algebra | |
dc.subject | Noncommutative integration | |
dc.subject | Operator algebra | |
dc.subject | Positive operator | |
dc.subject | Semifinite normal weight | |
dc.subject | Unbounded operator | |
dc.subject | Von Neumann algebra | |
dc.title | L1-space for a positive operator affiliated with von Neumann algebra | |
dc.type | Article in Press | |
dc.collection | Публикации сотрудников КФУ | |
dc.relation.startpage | 1 | |
dc.source.id | SCOPUS13851292-2016-SID84969791877 |