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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

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MathSciNet review: 1567199
Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: Charalambos D. Aliprantis and Owen Burkinshaw
Title: Locally solid Riesz spaces
Additional book information: Academic Press, New York, 1978, xii + 198 pp.

References [Enhancements On Off] (What's this?)

  • Ichirô Amemiya, A general spectral theory in semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 12 (1953), 111–156. MR 0056853
  • Ichiro Amemiya, On ordered topological linear spaces, Proc. Internat. Sympos. Linear Spaces (Jerusalem, 1960) Jerusalem Academic Press, Jerusalem; Pergamon, Oxford, 1961, pp. 14–23. MR 0138971
  • T. Andô, Contractive projections in $L_{p}$ spaces, Pacific J. Math. 17 (1966), 391–405. MR 192340
  • S. J. Bernau, Unique representation of Archimedean lattice groups and normal Archimedean lattice rings, Proc. London Math. Soc. (3) 15 (1965), 599–631. MR 182661, DOI 10.1112/plms/s3-15.1.599
  • S. J. Bernau, Lateral and Dedekind completion of Archimedean lattice groups, J. London Math. Soc. (2) 12 (1975/76), no. 3, 320–322. MR 401579, DOI 10.1112/jlms/s2-12.3.320
  • S. J. Bernau and H. Elton Lacey, The range of a contractive projection on an $L_{p}$-space, Pacific J. Math. 53 (1974), 21–41. MR 358325
  • S. J. Bernau and H. E. Lacey, Banach lattices and local unconditional structure, Notes in Banach spaces, Univ. Texas Press, Austin, Tex., 1980, pp. 405–426. MR 606227
  • Roger D. Bleier, Free vector lattices, Trans. Amer. Math. Soc. 176 (1973), 73–87. MR 311541, DOI 10.1090/S0002-9947-1973-0311541-8
  • F. Bohnenblust, An axiomatic characterization of $L_p$-spaces, Duke Math. J. 6 (1940), 627–640. MR 2701
  • N. Bourbaki, Eléments de mathématique. XIII. Première partie: Les structures fondamentales de l’analyse. Livre VI: Intégration. Chapitre I: Inégalités de convexité. Chapitre II: Espaces de Riesz. Chapitre III: Mesures sur les espaces localement compacts. Chapitre IV: Prolongement d’une mesure; espaces $L^p$, Actualités Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1175, Hermann & Cie, Paris, 1952 (French). MR 0054691
  • R. G. Douglas, Contractive projections on an ${\mathfrak {L}}_{1}$ space, Pacific J. Math. 15 (1965), 443–462. MR 187087
  • D. H. Fremlin, Topological Riesz spaces and measure theory, Cambridge University Press, London-New York, 1974. MR 0454575
    • 13.
    D. H. Fremlin, Review of Banach lattices and positive operators by H. H. Schaefer, Bull. London Math. Soc. 8 (1976), 215-216.
    14.
    H. Freudenthal, Teilweise geordnete Moduln, Nederl. Akad. Wetensch. Proc. Ser. A 39 (1936), 641-651.
  • A. Grothendieck, Une caractérisation vectorielle-métrique des espaces $L^1$, Canadian J. Math. 7 (1955), 552–561 (French). MR 76301, DOI 10.4153/CJM-1955-060-6
  • J. R. Isbell, A structure space for certain lattice-ordered groups and rings, J. London Math. Soc. 40 (1965), 63–71. MR 172940, DOI 10.1112/jlms/s1-40.1.63
  • Shizuo Kakutani, Concrete representation of abstract $(L)$-spaces and the mean ergodic theorem, Ann. of Math. (2) 42 (1941), 523–537. MR 4095, DOI 10.2307/1968915
  • Shizuo Kakutani, Concrete representation of abstract $(M)$-spaces. (A characterization of the space of continuous functions.), Ann. of Math. (2) 42 (1941), 994–1024. MR 5778, DOI 10.2307/1968778
    • 19.
    L. V. Kantorovich, Lineare halbgeordnete Raume, Mat. Sb. 44 (1937), 121-168.
  • H. Elton Lacey, Local unconditional structure in Banach spaces, Banach spaces of analytic functions (Proc. Pelczynski Conf., Kent State Univ., Kent, Ohio, 1976) Lecture Notes in Math., Vol. 604, Springer, Berlin, 1977, pp. 44–56. MR 0454596
  • Joram Lindenstrauss and Lior Tzafriri, Classical Banach spaces. II, Ergebnisse der Mathematik und ihrer Grenzgebiete [Results in Mathematics and Related Areas], vol. 97, Springer-Verlag, Berlin-New York, 1979. Function spaces. MR 540367
    • 22.
    W. A. J. Luxemburg, Notes on Banach function spaces, Nederl. Akad. Wetensch. Proc. Ser. A, Note XIV 68 (1965), 229-248; Note XV 68 (1965), 415-446; Note XVI 68 (1965), 646-667.
    23.
    W. A. J. Luxemburg and A. C. Zaanen, Notes on Banach Junction spaces, Nederl. Akad. Wetensch. Proc. Ser. A, Note 1 66 (1963), 135-147; Note II 66 (1963), 148-153; Note III 66 (1963), 239-250; Note IV 66 (1963), 251-263; Note V 66 (1963), 496-504; Note VI 66 (1963), 655-668; Note VII 66 (1963), 669-681; Note VIII 67 (1964), 104-119; Note IX 67 (1964), 360-376; Note X 67 (1964), 493-506; Note XI 67 (1964), 507-518; Note XII 67 (1964), 519-529; Note XIII 67 (1964), 530-543.
    24.
    W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces. I, North-Holland, Amsterdam, 1971.
  • Fumitomo Maeda and Tôzirô Ogasawara, Representation of vector lattices, J. Sci. Hiroshima Univ. Ser. A 12 (1942), 17–35 (Japanese). MR 29087
  • Hidegorô Nakano, Über das System aller stetigen Funktionen auf einem topologischen Raum, Proc. Imp. Acad. Tokyo 17 (1941), 308–310 (German). MR 14173
  • Hidegorô Nakano, Über normierte teilweisegeordnete Moduln, Proc. Imp. Acad. Tokyo 17 (1941), 311–317 (German). MR 14174
  • Hidegorô Nakano, Eine Spektraltheorie, Proc. Phys.-Math. Soc. Japan (3) 23 (1941), 485–511 (German). MR 5797
  • Hidegorô Nakano, Teilweise geordnete Algebra, Jpn. J. Math. 17 (1941), 425–511 (German). MR 5796, DOI 10.4099/jjm1924.17.0_{4}25
  • Hidegorô Nakano, Stetige lineare Funktionale auf dem teilweisegeordneten Modul, J. Fac. Sci. Imp. Univ. Tokyo Sect. I. 4 (1942), 201–382 (German). MR 0022308
  • Hidegorô Nakano, Modulared Semi-Ordered Linear Spaces, Maruzen Co. Ltd., Tokyo, 1950. MR 0038565
  • Hidegorô Nakano, Linear topologies on semi-ordered linear spaces, J. Fac. Sci. Hokkaido Univ. Ser. I. 12 (1953), 87–104. MR 0056851
  • Tôzirô Ogasawara, Theory of vector lattices. I, J. Sci. Hiroshima Univ. Ser. A 12 (1942), 37–100 (Japanese). MR 29089
    • 34.
    F. Riesz, Sur la décomposition des opérations fonctionelles linéaires, Atti del Congr. Internaz. dei Mat., Bologna 1928, 3 (1930), 143-148; Oeuvres Completes II, 1097-1102, Budapest, 1960.
  • Helmut H. Schaefer, Banach lattices and positive operators, Die Grundlehren der mathematischen Wissenschaften, Band 215, Springer-Verlag, New York-Heidelberg, 1974. MR 0423039
  • František Šik, Zur Theorie der halbgeordneten Gruppen, Czechoslovak Math. J. 6(81) (1956), 1–25 (Russian, with German summary). MR 81907
    • 37.
    S. W. P. Steen, An introduction to the theory of operators. I, Proc. London Math. Soc. (2) 41 (1936), 361-392.
  • M. H. Stone, A general theory of spectra. I, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 280–283. MR 2023, DOI 10.1073/pnas.26.4.280
  • L. Tzafriri, Remarks on contractive projections in $L_{p}$-spaces, Israel J. Math. 7 (1969), 9–15. MR 248514, DOI 10.1007/BF02771741
  • Kôsaku Yosida, On vector lattice with a unit, Proc. Imp. Acad. Tokyo 17 (1941), 121–124. MR 5795
  • Kôsaku Yosida, Vector lattices and additive set functions, Proc. Imp. Acad. Tokyo 17 (1941), 228–232. MR 8119
  • Kôsaku Yosida, On the representation of the vector lattice, Proc. Imp. Acad. Tokyo 18 (1942), 339–342. MR 15378
    •
    Review Information:

    Reviewer: Simon J. Bernau
    Journal: Bull. Amer. Math. Soc. 1 (1979), 997-1003
    DOI: https://doi.org/10.1090/S0273-0979-1979-14715-3