Previous |  Up |  Next

Article

Keywords:
Orlicz spaces; von Neumann algebra; weight
Summary:
Let $M$ be a von Neumann algebra, let $\varphi$ be a weight on $M$ and let $\Phi$ be $N$-function satisfying the $(\delta_{2}, \Delta_{2})$-condition. In this paper we study Orlicz spaces, associated with $M$, $\varphi$ and $\Phi $.
References:
[1] Al-Rashed M.H.A., Zegarlinski B.: Noncommutative Orlicz spaces associated to a state. Studia Math. 180 (2007), 199–209. MR 2314076 | Zbl 1221.46065
[2] Brawn L.G., Kosaki H.: Jensen's inequality in semi-finite von Neumann algebras. J. Operator Theory 23 (1990), 3–19. MR 1054812
[3] Fack T., Kosaki H.: Generalized $s$-number of $\tau$-measurable operators. Pacific J. Math. 123 (1986), 269–300. DOI 10.2140/pjm.1986.123.269 | MR 0840845
[4] Krasnosel'sky M.F., Rutitskii Ya.B.: Convex Functions and Orlicz Spaces. Noordhoff, Groningen, 1961; (translated from the Russian). MR 0126722
[5] Kunze W.: Noncommutative Orlicz spaces and generalized Arens algebras. Math. Nachr. 147 (1990), 123–138. DOI 10.1002/mana.19901470114 | MR 1127316 | Zbl 0746.46062
[6] Muratov M.A.: Non commutative Orlicz spaces. Dokl. Akad. Nauk UzSSR 6 (1978), 11–13. MR 0511082
[7] Muratov M.A.: The Luxemburg norm in an Orlicz space of measurable operators. Dokl. Akad. Nauk UzSSR 1 (1979), 5–6. MR 0529172
[8] Muratov M.A., Chilin V.I.: Algebras of measurable operators and locally measurable operators. Kyev. Institute of Math. Ukrainian Academy of Sciences, 69, 2007 (Russian).
[9] Pedersen G., Takesaki M.: The Radon-Nikodym theorem for von Neumann algebras. Acta Math. 130 (1973), 53–87. DOI 10.1007/BF02392262 | MR 0412827 | Zbl 0262.46063
[10] Takesaki M.: Theory of Operator Algebras I. Springer, New York, 1979. MR 0548728 | Zbl 0990.46034
[11] Trunov N.V.: The $L_p$-spaces associated with a weight on a semi-finite von Neumann algebra. Constructive theory of functions and functional analysis, no. 3, pp. 88–93, Kazan. Gos. Univ., Kazan, 1981. MR 0652348
[12] Trunov N.V.: On the theory of normal weights on von Neumann algebras. Izv. Vyssh. Uchebn. Zaved. Math. 8 1982, 61–70. MR 0675719 | Zbl 0521.46056
[13] Trunov N.V., Sherstnev A.N.: Introduction to the theory of noncommutative integration. N. Soviet Math., 37. Translation from Itogi Nauki i Tekhniki, Sovr. Probl. Math. 27 (1985), 167–190. MR 0824264 | Zbl 0616.46058
[14] Yeadon F.J.: Convergence of measurable operators. Proc. Cambridge Philos. Soc. 74 (1973), 257–268. MR 0326411 | Zbl 0272.46043
[15] Yeadon F.J.: Non-commutative $L^{p}$-spaces. Math. Proc. Cambridge Philos. Soc. 77 (1975), no. 1, 91–102. DOI 10.1017/S0305004100049434 | MR 0353008
Partner of
EuDML logo