An Analytic Representation of the $L_0$-Valued Homomorphisms in the Orlicz--Kantorovich Modules
Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 112-141.

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We consider the Orlicz–Kantorovich modules $L_M(\nabla,m)$ associated with a complete Boolean algebra $\nabla$, an $N$-function $M$, and a measure $m$ defined on $\nabla$ and taking values in the algebra $L_0$ of all measurable real functions. We obtain an analytic representation of the continuous $L_0$-valued homomorphisms defined on such modules.
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B. S. Zakirov. An Analytic Representation of the $L_0$-Valued Homomorphisms in the Orlicz--Kantorovich Modules. Matematičeskie trudy, Tome 10 (2007) no. 2, pp. 112-141. http://geodesic.mathdoc.fr/item/MT_2007_10_2_a4/

[1] Vladimirov D. A., Bulevy algebry, Nauka, M., 1969 | MR

[2] Vulikh B. Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, Fizmatgiz, M., 1961 | MR

[3] Gutman A. E., “Banakhovy rassloeniya v teorii reshetochno normirovannykh prostranstv”, Lineinye operatory, soglasovannye s poryadkom, Izd-vo IM SO RAN, Novosibirsk, 1995, 63–211 | MR

[4] Zakirov B. S., “Norma Lyuksemburga v reshetke Orlicha — Kantorovicha”, Uzbekskii mat. zhurn., 2007, no. 2, 32–44 | MR

[5] Zakirov B. S., “Reshetki Orlicha — Kantorovicha, assotsiirovannye s $L_0$-znachnoi meroi”, Uzbekskii mat. zhurn., 2007, no. 4, 35–51

[6] Krasnoselskii M. A., Rutitskii Ya. B., Vypuklye funktsii i prostranstva Orlicha, Fizmatgiz, M., 1958 | MR

[7] Kusraev A. G., Vektornaya dvoistvennost i ee prilozheniya, Novosibirsk, 1985 | MR

[8] Kusraev A. G., Mazhoriruemye operatory, Nauka, M., 2003 | MR

[9] Sarymsakov T. A., Topologicheskie polupolya i ikh prilozheniya, Fan, Tashkent, 1989 | MR | Zbl