A non-commutative version of Nikishin’s theorem

Let τ be a tracial normal state on a von Neumann algebra, L1(τ) be the space of integrable self-adjoint operators, and S be the space of self-adjoint measurable operators. We prove that every positive linear operator from an ordered Banach space to S can be factorized through L1(τ).

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Podrobná bibliografie
Vydáno v:	Indagationes mathematicae Ročník 26; číslo 1; s. 142 - 146
Hlavní autoři:	Tikhonov, O.E., Veselova, L.V.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Elsevier B.V 01.01.2015
Témata:	Factorization of operators Measurable operator Positive operator Tracial normal state von Neumann algebra Measurable operator Factorization of operators Tracial normal state von Neumann algebra Positive operator
ISSN:	0019-3577, 1872-6100
On-line přístup:	Získat plný text
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Popis
Shrnutí:	Let τ be a tracial normal state on a von Neumann algebra, L1(τ) be the space of integrable self-adjoint operators, and S be the space of self-adjoint measurable operators. We prove that every positive linear operator from an ordered Banach space to S can be factorized through L1(τ).
ISSN:	0019-3577 1872-6100
DOI:	10.1016/j.indag.2014.09.001