| Title:
|
Representations of Riesz spaces as spaces of measures. I (English) |
| Author:
|
Filter, Wolfgang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
42 |
| Issue:
|
3 |
| Year:
|
1992 |
| Pages:
|
415-432 |
| . |
| Category:
|
math |
| . |
| MSC:
|
28A33 |
| MSC:
|
46A40 |
| MSC:
|
46E27 |
| idZBL:
|
Zbl 0803.46008 |
| idMR:
|
MR1179304 |
| DOI:
|
10.21136/CMJ.1992.128351 |
| . |
| Date available:
|
2009-09-24T09:22:35Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128351 |
| . |
| Reference:
|
[AB] C. D. Aliprantis and O. Burkinshaw: Locally solid Riesz spaces.Academic Press, New York-San Francisco-London, 1978. MR 0493242 |
| Reference:
|
[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 |
| Reference:
|
[BK] H. F. Bohnenblust and S. Kakutani: Concrete representation of $(M)$-spaces.Ann. of Math. 42 (1941), 1025–1028. MR 0005779, 10.2307/1968779 |
| Reference:
|
[BN] L. Brown and H. Nakano: A representation theorem for Archimedean linear lattices.Proc. Amer. Math. Soc. 17 (1966), 835–837. MR 0193484, 10.1090/S0002-9939-1966-0193484-8 |
| Reference:
|
[BR] G. Buskes and A. van Rooij: Small Riesz spaces.Math. Proc. Cambridge Philos. Soc. 105 (1989), 523–536. MR 0985689, 10.1017/S0305004100077902 |
| Reference:
|
[C] C. Constantinescu: Duality in measure theory.LN in mathematics 796, Springer-Verlag, Berlin-Heidelberg-New York, 1980. Zbl 0429.28009, MR 0574273 |
| Reference:
|
[D] E. B. Davies: The Choquet theory and representation of ordered Banach spaces.Illinois J. Math. 13 (1969), 176–187. Zbl 0165.46801, MR 0235399, 10.1215/ijm/1256053750 |
| Reference:
|
[FP1] W. A. Feldman and J. F. Porter: Banach lattices with locally compact representation spaces.Math. Z. 174 (1980), 233–239. MR 0593822, 10.1007/BF01161412 |
| Reference:
|
[FP2] W. A. Feldman and J. F. Porter: Uniqueness of representation spaces.Math. Z. 179 (1982), 213–217. MR 0645497, 10.1007/BF01214313 |
| Reference:
|
[Fi1] W. Filter: A note on Archimedean Riesz spaces and their extended order duals.Libertas Math. 6 (1986), 101–106. Zbl 0612.46007, MR 0848304 |
| Reference:
|
[Fi2] W. Filter: Atomical and atomfree elements of a Riesz space.Arch. Math. (Basel) 52 (1989), 580–587. Zbl 0659.46004, MR 1007633, 10.1007/BF01237571 |
| Reference:
|
[Fi3] W. Filter: Hypercomplete Riesz spaces.Atti Sem. Mat. Fis. Univ. Modena 38 (1990), 227–240. Zbl 0716.46008, MR 1122681 |
| Reference:
|
[Fi4] W. Filter: Hypercompletions of Riesz spaces.Proc. Amer. Math. Soc. 109 (1990), 775–780. Zbl 0716.46009, MR 1021210, 10.1090/S0002-9939-1990-1021210-2 |
| Reference:
|
[Fi5] W. Filter: Hellinger–type integrals in Riesz spaces.Houston J. Math. 17 (1991), 179–200. Zbl 0778.46009, MR 1115142 |
| Reference:
|
[Fi6] W. Filter: Measurability and decomposition properties in the dual of a Riesz space.Rend. Circ. Mat. Palermo, Suppl. Volume (to appear). Zbl 0780.46006, MR 1183038 |
| Reference:
|
[Fl] I. Fleischer: Functional representation of vector lattices.Proc. Amer. Math. Soc. 108 (1990), 471–478. Zbl 0743.46005, MR 0993750, 10.1090/S0002-9939-1990-0993750-3 |
| Reference:
|
[Fr1] D. H. Fremlin: Abstract Köthe spaces. II.Proc. Cambridge Philos. Soc. 63 (1967), 951–956. MR 0216272, 10.1017/S0305004100041979 |
| Reference:
|
[Fr2] D. H. Fremlin: Topological Riesz spaces and measure theory.Cambridge Univ. Press, London-New York, 1974. Zbl 0273.46035, MR 0454575 |
| Reference:
|
[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 |
| Reference:
|
[H1] W. Hackenbroch: Zur Darstellungstheorie $\sigma $-vollständiger Vektorverbände.Math. Z. 128 (1972), 115–128. Zbl 0231.46017, MR 0324366, 10.1007/BF01111473 |
| Reference:
|
[H2] W. Hackenbroch: Eindeutigkeit des Darstellungsraumes von Vektorverbänden.Math. Z. 135 (1974), 285–288. Zbl 0263.46007, MR 0348439, 10.1007/BF01215367 |
| Reference:
|
[JK1] D. G. Johnson and J. E. Kist: Complemented ideals and extremally disconnected spaces.Arch. Math. (Basel) 12 (1961), 349–354. MR 0148575, 10.1007/BF01650573 |
| Reference:
|
[JK2] D. G. Johnson and J. E. Kist: Prime ideals in vector lattices.Canad. J. Math. 14 (1962), 517–528. MR 0138566, 10.4153/CJM-1962-043-3 |
| Reference:
|
[Ka1] S. Kakutani: Concrete representation of abstract $L$-spaces and the mean ergodic theorem.Ann. of Math. 42 (1941), 523–537. Zbl 0027.11102, MR 0004095, 10.2307/1968915 |
| Reference:
|
[Ka2] S. Kakutani: Concrete representation of abstract $M$-spaces.Ann. of Math. 42 (1941), 994–1024. Zbl 0060.26604, MR 0005778, 10.2307/1968778 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[L] I. Labuda: Submeasures and locally solid topologies on Riesz spaces.Math. Z. 195 (1987), 179–196. Zbl 0601.46006, MR 0892050, 10.1007/BF01166456 |
| Reference:
|
[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. MR 0212540, 10.4153/CJM-1967-041-6 |
| Reference:
|
[LZ] W. A. J. Luxemburg and A. C. Zaanen: Riesz spaces I.North-Holland Publ. Comp., Amsterdam -London, 1971. MR 0511676 |
| Reference:
|
[MO] F. Maeda and T. Ogasawara: Representation of vector lattices.J. Sci. Hiroshima Univ. Ser. A 12 (1942), 17–35. (Japanese) MR 0029087, 10.32917/hmj/1558306491 |
| Reference:
|
[MW] B. M. Makarov and M. Weber: On the realization of vector lattices I.Math. Nachr. 60 (1974), 281–296. (Russian) MR 0372580 |
| Reference:
|
[M] J. T. Marti: Topological representation of abstract $L_p$-spaces.Math. Ann. 185 (1970), 315–321. MR 0261318, 10.1007/BF01349954 |
| Reference:
|
[N] H. Nakano: Eine Spektraltheorie.Proc. Phys.-Math. Soc. Japan (3) 23 (1941), 485–511. Zbl 0060.26504, MR 0005797 |
| Reference:
|
[O] T. Ogasawara: Remarks on the representation of vector lattices.J. Sci. Hiroshima Univ. Ser. A 12 (1943), 217–234. (Japanese) MR 0029088, 10.32917/hmj/1559145789 |
| Reference:
|
[P] A. G. Pinsker: On concrete representations of linear semi-ordered spaces.C. R. (Doklady) Acad. Sci. URSS (N. S.) 55 (1947), 379–381. Zbl 0029.04903, MR 0021661 |
| Reference:
|
[Sc1] H. H. Schaefer: On the representation of Banach lattices by continuous numerical functions.Math. Z. 125 (1972), 215–232. Zbl 0216.40702, MR 0298389, 10.1007/BF01111305 |
| Reference:
|
[Sc2] H. H. Schaefer: Banach lattices and positive operators.Springer-Verlag, New York-Heidelberg-Berlin, 1974. Zbl 0296.47023, MR 0423039 |
| Reference:
|
[Se] Z. Semadeni: Banach spaces of continuous functions I.Polish Scientific Publ., Warsaw, 1971. MR 0296671 |
| Reference:
|
[Ve1] A. I. Veksler: Realizations of Archimedean $K$-lineals.Sibirsk. Mat. Zh. 3 (1962), 7–16. (Russian) MR 0150063 |
| Reference:
|
[Ve2] A. I. Veksler: Localness of functional vector lattices.Siberian Math. J. 12 (1971), 39–46. MR 0295048, 10.1007/BF00969139 |
| Reference:
|
[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 |
| Reference:
|
[Vi] V. K. Vietsch: Abstract kernel operators and compact operators.Ph. D. thesis, Leiden Univ., 1979. |
| Reference:
|
[Vu] B. Z. Vulikh: Concrete representations of linear partially ordered spaces.Dokl. Akad. Nauk SSSR 58 (1947), 733-736. (Russian) MR 0022992 |
| Reference:
|
[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. 10.1070/SM1971v013n03ABEH003686 |
| Reference:
|
[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. Zbl 0434.06017, MR 0540584 |
| Reference:
|
[Wo] M. Wolff: Darstellung von Banach-Verbänden und Sätze vom Korovkin-Typ.Math. Ann. 200 (1973), 47–67. Zbl 0236.46010, MR 0328542, 10.1007/BF01578291 |
| Reference:
|
[Wn] W. Wnuk: Representations of Orlicz lattices.Diss. Math. 235 (1984). Zbl 0566.46018, MR 0820077 |
| Reference:
|
[Y] K. Yosida: On the representation of the vector lattice.Proc. Imp. Acad. Tokyo 18 (1941-42), 339–342. Zbl 0063.09070, MR 0015378 |
| Reference:
|
[Z] A. C. Zaanen: Riesz spaces II.North-Holland Publ. Comp., Amsterdam-New York-London, 1983. Zbl 0519.46001, MR 0704021 |
| . |
