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• W2256309348 abstract "In this paper we suggest an approach for constructing an L1-type space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we intro- duce a seminorm, and prove that it is a norm if and only if the operator is injective. For this norm we construct an L1 -type space as the complition of the space of hermitian ultraweakly continuous linear functionals on von Neumann algebra, and represent L1- type space as a space of continuous linear functionals on the space of special sesquilinear forms. Also, we prove that L1 -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 L1-type space, and demonstrate the con- nection 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 L1 -type space in case when this C*-algebra is a von Neumann algebra." @default.
• W2256309348 created "2016-06-24" @default.
• W2256309348 creator A5080217041 @default.
• W2256309348 date "2016-05-18" @default.
• W2256309348 modified "2023-09-23" @default.
• W2256309348 title "$$L_1$$ L 1 -space for a positive operator affiliated with von Neumann algebra" @default.
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• W2256309348 doi "https://doi.org/10.1007/s11117-016-0422-4" @default.
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