Previous |  Up |  Next

Article

References:
[AB] C. D. Aliprantis and O. Burkinshaw: Locally solid Riesz spaces. Academic Press, New York-San Francisco-London, 1978. MR 0493242
[B] S. J. Bernau: Unique representation of Archimedean lattice groups and normal Archimedean lattice rings. Proc. London Math. Soc. (3) 15 (1965), 599–631. MR 0182661
[BK] H. F. Bohnenblust and S. Kakutani: Concrete representation of $(M)$-spaces. Ann. of Math. 42 (1941), 1025–1028. DOI 10.2307/1968779 | MR 0005779
[BN] L. Brown and H. Nakano: A representation theorem for Archimedean linear lattices. Proc. Amer. Math. Soc. 17 (1966), 835–837. DOI 10.1090/S0002-9939-1966-0193484-8 | MR 0193484
[BR] G. Buskes and A. van Rooij: Small Riesz spaces. Math. Proc. Cambridge Philos. Soc. 105 (1989), 523–536. DOI 10.1017/S0305004100077902 | MR 0985689
[C] C. Constantinescu: Duality in measure theory. LN in mathematics 796, Springer-Verlag, Berlin-Heidelberg-New York, 1980. MR 0574273 | Zbl 0429.28009
[D] E. B. Davies: The Choquet theory and representation of ordered Banach spaces. Illinois J. Math. 13 (1969), 176–187. MR 0235399 | Zbl 0165.46801
[FP1] W. A. Feldman and J. F. Porter: Banach lattices with locally compact representation spaces. Math.  Z. 174 (1980), 233–239. DOI 10.1007/BF01161412 | MR 0593822
[FP2] W. A. Feldman and J. F. Porter: Uniqueness of representation spaces. Math. Z. 179 (1982), 213–217. DOI 10.1007/BF01214313 | MR 0645497
[Fi1] W. Filter: A note on Archimedean Riesz spaces and their extended order duals. Libertas Math. 6 (1986), 101–106. MR 0848304 | Zbl 0612.46007
[Fi2] W. Filter: Atomical and atomfree elements of a Riesz space. Arch. Math. (Basel) 52 (1989), 580–587. DOI 10.1007/BF01237571 | MR 1007633 | Zbl 0659.46004
[Fi3] W. Filter: Hypercomplete Riesz spaces. Atti Sem. Mat. Fis. Univ. Modena 38 (1990), 227–240. MR 1122681 | Zbl 0716.46008
[Fi4] W. Filter: Hypercompletions of Riesz spaces. Proc. Amer. Math. Soc. 109 (1990), 775–780. DOI 10.1090/S0002-9939-1990-1021210-2 | MR 1021210 | Zbl 0716.46009
[Fi5] W. Filter: Hellinger–type integrals in Riesz spaces. Houston J. Math. 17 (1991), 179–200. MR 1115142 | Zbl 0778.46009
[Fi6] W. Filter: Measurability and decomposition properties in the dual of a Riesz space. Rend. Circ. Mat. Palermo, Suppl. Volume (to appear). MR 1183038 | Zbl 0780.46006
[Fl] I. Fleischer: Functional representation of vector lattices. Proc. Amer. Math. Soc. 108 (1990), 471–478. DOI 10.1090/S0002-9939-1990-0993750-3 | MR 0993750 | Zbl 0743.46005
[Fr1] D. H. Fremlin: Abstract Köthe spaces. II. Proc. Cambridge Philos. Soc. 63 (1967), 951–956. DOI 10.1017/S0305004100041979 | MR 0216272
[Fr2] D. H. Fremlin: Topological Riesz spaces and measure theory. Cambridge Univ. Press, London-New York, 1974. MR 0454575 | Zbl 0273.46035
[G] A. Goullet de Rugy: Representation of Banach lattices. Foundations of quantum mechanics and ordered linear spaces, LN in Physics 29, Springer-Verlag, Berlin-Heidelberg-New York, 1974, pp. 41–46. MR 0487384
[H1] W. Hackenbroch: Zur Darstellungstheorie $\sigma $-vollständiger Vektorverbände. Math. Z. 128 (1972), 115–128. DOI 10.1007/BF01111473 | MR 0324366 | Zbl 0231.46017
[H2] W. Hackenbroch: Eindeutigkeit des Darstellungsraumes von Vektorverbänden. Math. Z. 135 (1974), 285–288. DOI 10.1007/BF01215367 | MR 0348439 | Zbl 0263.46007
[JK1] D. G. Johnson and J. E. Kist: Complemented ideals and extremally disconnected spaces. Arch. Math. (Basel) 12 (1961), 349–354. DOI 10.1007/BF01650573 | MR 0148575
[JK2] D. G. Johnson and J. E. Kist: Prime ideals in vector lattices. Canad. J. Math. 14 (1962), 517–528. DOI 10.4153/CJM-1962-043-3 | MR 0138566
[Ka1] S. Kakutani: Concrete representation of abstract $L$-spaces and the mean ergodic theorem. Ann. of Math. 42 (1941), 523–537. DOI 10.2307/1968915 | MR 0004095 | Zbl 0027.11102
[Ka2] S. Kakutani: Concrete representation of abstract $M$-spaces. Ann. of Math. 42 (1941), 994–1024. DOI 10.2307/1968778 | MR 0005778 | Zbl 0060.26604
[Ko] A. V. Koldunov: Strict realization of vector lattices. Theory of functions and functional analysis, Leningrad. Gos. Ped. Inst., Leningrad, 1975, pp. 67–74. (Russian) MR 0625330
[KK1] M. G. Kreĭn and S. G. Kreĭn: On an inner characteristic of the set of all continuous functions defined on a bicompact Hausdorff space. Dokl. Akad. Nauk SSSR 27 (1940), 427–430. (Russian) MR 0003453
[KK2] M. G. Kreĭn and S. G. Kreĭn: Sur  l’espace  des  fonctions  continues   définies  sur  un  bicompact  de  Hausdorff  et  ses  sous- espaces semi-ordonnés. Mat. Sb. 13(55) (1943), 1–38. MR 0012209
[L] I. Labuda: Submeasures and locally solid topologies on Riesz spaces. Math. Z. 195 (1987), 179–196. DOI 10.1007/BF01166456 | MR 0892050 | Zbl 0601.46006
[LM] W. A. J. Luxemburg and J. J. Masterson: An extension of the concept of the order dual of a Riesz space. Canad. J. Math. 19 (1967), 488–498. DOI 10.4153/CJM-1967-041-6 | MR 0212540
[LZ] W. A. J. Luxemburg and A. C. Zaanen: Riesz spaces I. North-Holland Publ. Comp., Amsterdam -London, 1971. MR 0511676
[MO] F. Maeda and T. Ogasawara: Representation of vector lattices. J. Sci. Hiroshima Univ. Ser. A 12 (1942), 17–35. (Japanese) MR 0029087
[MW] B. M. Makarov and M. Weber: On the realization of vector lattices I. Math. Nachr. 60 (1974), 281–296. (Russian) MR 0372580
[M] J. T. Marti: Topological representation of abstract $L_p$-spaces. Math. Ann. 185 (1970), 315–321. DOI 10.1007/BF01349954 | MR 0261318
[N] H. Nakano: Eine Spektraltheorie. Proc. Phys.-Math. Soc. Japan (3) 23 (1941), 485–511. MR 0005797 | Zbl 0060.26504
[O] T. Ogasawara: Remarks on the representation of vector lattices. J. Sci. Hiroshima Univ. Ser. A 12 (1943), 217–234. (Japanese) MR 0029088
[P] A. G. Pinsker: On concrete representations of linear semi-ordered spaces. C. R. (Doklady) Acad. Sci. URSS (N. S.) 55 (1947), 379–381. MR 0021661 | Zbl 0029.04903
[Sc1] H. H. Schaefer: On the representation of Banach lattices by continuous numerical functions. Math. Z. 125 (1972), 215–232. DOI 10.1007/BF01111305 | MR 0298389 | Zbl 0216.40702
[Sc2] H. H. Schaefer: Banach lattices and positive operators. Springer-Verlag, New York-Heidelberg-Berlin, 1974. MR 0423039 | Zbl 0296.47023
[Se] Z. Semadeni: Banach spaces of continuous functions I. Polish Scientific Publ., Warsaw, 1971. MR 0296671
[Ve1] A. I. Veksler: Realizations of Archimedean $K$-lineals. Sibirsk. Mat. Zh. 3 (1962), 7–16. (Russian) MR 0150063
[Ve2] A. I. Veksler: Localness of functional vector lattices. Siberian Math. J. 12 (1971), 39–46. DOI 10.1007/BF00969139 | MR 0295048
[Ve3] A. I. Veksler: The Kreĭn-Kakutani Theorem and realization characteristics of $K_{\sigma }$-spaces. Functional analysis, No. 9: Harmonic analysis on groups, Ul’janovsk. Gos. Ped. Inst., Ul’yanovsk, 1977, pp. 8–16. (Russian) MR 0625486
[Vi] V. K. Vietsch: Abstract kernel operators and compact operators. Ph. D. thesis, Leiden Univ., 1979.
[Vu] B. Z. Vulikh: Concrete representations of linear partially ordered spaces. Dokl. Akad. Nauk SSSR 58 (1947), 733-736. (Russian) MR 0022992
[VL] B. Z. Vulikh and G. Ya. Lozanovskiĭ: On the representation of completely linear and regular functionals in partially ordered spaces. Math. USSR-Sb. 13 (1971), 323–343. DOI 10.1070/SM1971v013n03ABEH003686
[We] M. Weber: On the realization of vector lattices on locally compact topological spaces. Proc. Conf. Topology and Measure I, Wissensch. Beitr. Ernst-Moritz-Arndt-Univ. Greifswald, 1978, pp. 393–401. MR 0540584 | Zbl 0434.06017
[Wo] M. Wolff: Darstellung von Banach-Verbänden und Sätze vom Korovkin-Typ. Math. Ann. 200 (1973), 47–67. DOI 10.1007/BF01578291 | MR 0328542 | Zbl 0236.46010
[Wn] W. Wnuk: Representations of Orlicz lattices. Diss. Math. 235 (1984). MR 0820077 | Zbl 0566.46018
[Y] K. Yosida: On the representation of the vector lattice. Proc. Imp. Acad. Tokyo 18 (1941-42), 339–342. MR 0015378 | Zbl 0063.09070
[Z] A. C. Zaanen: Riesz spaces II. North-Holland Publ. Comp., Amsterdam-New York-London, 1983. MR 0704021 | Zbl 0519.46001
Partner of
EuDML logo