On the representation of completely linear and regular functionals in partially ordered spaces
Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 323-343 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the first two sections the representation of completely linear functionals in $K$-spaces and the connection between completely linear functionals and measures on bases in a $K$-space is studied. In § 3 a realization of spaces of regular functionals is established. Bibliography: 15 titles.
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B. Z. Vulikh; G. Ya. Lozanovskii. On the representation of completely linear and regular functionals in partially ordered spaces. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 323-343. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a0/

[1] N. Burbaki, Integrirovanie, Nauka, Moskva, 1967 | MR

[2] B. Z. Vulikh, Vvedenie v teoriyu poluuporyadochennykh prostranstv, Fizmatgiz, Moskva, 1961

[3] N. Danford, Dzh. T. Shvarts, Lineinye operatory, t. 1, IL, Moskva, 1962

[4] J. Dixmier, “Sur certains espaces considérés par M. H. Stone”, Summa Brasil. Mathu, 2 (1951), 151–182 | MR | Zbl

[5] K. Yosida, “On the theory of spectra”, Proc. Acad. Tokyo, 16 (1940), 378–383 | MR | Zbl

[6] S. Kakutani, “Concrete representation of abstract $(L)$-spaces and the mean ergodic theorem”, Ann. Math., 42 (1941), 523–537 | DOI | MR | Zbl

[7] L. V. Kantorovich, B. Z. Vulikh, A. G. Pinsker, Funktsionalnyi analiz v poluuporyadochennykh prostranstvakh, Gostekhizdat, Moskva–Leningrad, 1950 | Zbl

[8] J. L. Kelley, “Measures on Boolean algebras”, Pacif. J. Math., 9 (1959), 1165–1178 | MR

[9] J. L. Kelley, “Decomposition and representation theorems in measure theory”, Math. Ann., 163 (1966), 89–84 | DOI | MR

[10] G. Ya. Lozanovskii, “O banakhovykh strukturakh Kalderona”, DAN SSSR, 172:5 (1967), 1018–1020 | MR | Zbl

[11] G. Ya. Lozanovskii, “O realizatsii prostranstv regulyarnykh funktsionalov i nekotorykh ee primeneniyakh”, DAN SSSR, 188:3 (1969), 522–524 | MR | Zbl

[12] N. M. Rice, “Multiplication in vector lattices”, Canad. J. Math., 20 (1968), 1136–1149 | MR | Zbl

[13] I. E. Segal, “Equivalence of measure spaces”, Amer. J. Math., 73 (1951), 275–313 | DOI | MR | Zbl

[14] P. Sikorskii, Bulevy algebry, Mir, Moskva, 1969 | MR

[15] J. Schwartz, “A note on the space $L_p^*$”, Proc. Amer. Math. Soc., 2 (1951), 270–275 | DOI | MR | Zbl