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Book Review

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Book Information:

Author: Peter Meyer-Nieberg
Title: Banach lattices
Additional book information: Springer-Verlag, New York, 1991, 395 pp., US$49.95. ISBN 3-540-54201-9.

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

  • [1] C. D. Aliprantis, D. J. Brown, and O. Burkinshaw, Existence and optimality of competitive equilibria, Springer-Verlag, Heidelberg and New York, 1990. MR 1075992 (92i:90023)
  • [2] C. D. Aliprantis and O. Burkinshaw, Locally solid Riesz spaces, Academic Press, New York and London, 1978. MR 58 #12271 MR 0493242 (58:12271)
  • [3] -, Positive operators, Academic Press, New York and London, 1985. MR 87h:47086 MR 809372 (87h:47086)
  • [4] W. Arendt et al., One-parameter semigroups of positive operators, Lecture Notes in Math., vol. 1184, Springer-Verlag, Berlin and New York, 1986. MR 88i:47022 MR 839450 (88i:47022)
  • [5] S. Banach, Théorie des opérations linéaires, Monograf. Mat. 1 (1932), PWN, Warsaw. (Reprinted by Chelsea Publishing Co., New York, 1955.) Zbl 5, 209 MR 0071726 (17:175h)
  • [6] G. Birkhoff, Lattice theory, 3rd ed., Amer. Math. Soc. Colloq. Publ., vol. 25, Amer. Math. Soc., Providence, RI, 1967. MR 37 #2638 MR 0227053 (37:2638)
  • [7] -, Reactor criticality in transport theory, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 567-569. MR 21 #3131 MR 0104376 (21:3131)
  • [8] -, Positivity and criticality, Proc. Sympos. Appl. Math., vol. 10, Amer. Math. Soc., Providence, RI, 1961, pp. 116-126. MR 22 #11563 MR 0120814 (22:11563)
  • [9] R. Bürger, Mutation-selection and continuum-of-Alleles models, Math. Biosci. 91 (1988), 6783.
  • [10] P. G. Dodds and D. H. Fremlin, Compact operators in Banach lattices, Israel J. Math. 34 (1979), 287-320. MR 81g:47037 MR 570888 (81g:47037)
  • [11] D. H. Fremlin, Topological Riesz spaces and measure theory, Cambridge Univ. Press, London and New York, 1974. MR 56 #12824 MR 0454575 (56:12824)
  • [12] H. Freudenthal, Teilweise geordnete Moduln, Nederl. Akad. Wetensch. Proc. Ser. A 39 (1936), 641-651. Zbl 14, 313
  • [13] G. Jameson, Ordered linear spaces, Lecture Notes in Math., vol. 141, Springer-Verlag, Berlin and New York, 1970. MR 55 #10996 MR 0438077 (55:10996)
  • [14] W. Hildenbrand and H. Sonnenschein (eds.), Handbook of mathematical economics, vol. IV, North-Holland, Amsterdam and New York, 1991. MR 1207188 (95a:90001)
  • [15] L. V. Kantorovich, Concerning the general theory of operations in partially ordered spaces, Dokl. Akad. Nauk SSSR 1 (1936), 283-286. (Russian) Zbl 14, 67
  • [16] -, Lineare Halbgeordnete Räume, Mat. Sb. (N.S.) 49 (1940), 209-284. MR 2, 317
  • [17] S. Kaplan, The bidual of $ {C(X)}$, I, North-Holland, Amsterdam and New York, 1985. MR 86k:46001. MR 776606 (86k:46001)
  • [18] H. E. Lacey, The isometric theory of classical Banach spaces, Springer-Verlag, Berlin and New York, 1974. MR 58 #12308 MR 0493279 (58:12308)
  • [19] L. Le Cam, Asymptotic methods in statistical decision theory, Springer-Verlag, New York and Berlin, 1986. MR 88a:62004 MR 856411 (88a:62004)
  • [20] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces, II, Springer-Verlag, Berlin and New York, 1979. MR 81c:46001 MR 540367 (81c:46001)
  • [21] W. A. J. Luxemburg and A. C. Zaanen, Riesz spaces, I, North-Holland, Amsterdam, 1971. MR 58 #23483
  • [22] R. J. Nagel, Order in pure and applied functional analysis, Trends in functional analysis and approximation theory (Acquafredda di Maratea, 1989), Univ. of Modena, Modena, 1991, pp. 87-1001. MR 1136587 (92m:47071)
  • [23] H. Nakano, Modern spectral theory, Maruzen Co., Tokyo, 1950. MR 12, 419 MR 0038564 (12:419f)
  • [24] -, Modulared semi-ordered linear spaces, Maruzen Co., Tokyo, 1950. MR 12, 420 MR 0038565 (12:420a)
  • [25] A. L. Peressini, Ordered topological vector spaces, Harper & Row, New York, 1967. MR 37 #3315 MR 0227731 (37:3315)
  • [26] F. Riesz, Sur la décomposition des opérations linéaires, Atti Congr. Internaz. Mat. 3 (1930), 143-148.
  • [27] -, Sur quelques notions fondamentales dans la théorie générale des opérations linéaires, Ann. of Math. 41 (1940), 174-206. MR 1, 147 MR 0000902 (1:147d)
  • [28] H. H. Schaefer, Topological vector spaces, Springer-Verlag, Berlin and New York, 1971. MR 33 #1689 MR 0342978 (49:7722)
  • [29] -, Banach lattices and positive operators, Springer-Verlag, Berlin and New York, 1974. MR 54 #11023 MR 0423039 (54:11023)
  • [30] H.-U. Schwarz, Banach lattices and operators, Teubner-Texte Math., vol. 71, Teubner, Leipzig, 1984. MR 86h:46034 MR 781131 (86h:46034)
  • [31] B. Z. Vulikh, Introduction to the theory of partially ordered spaces, Wolter-Hoordhoff, Groningen, Netherlands, 1967. MR 24 #A3494 MR 0224522 (37:121)
  • [32] Y. C. Wong and K. F. Ng, Partially ordered topological vector spaces, Clarendon Press, Oxford, 1973. MR 56 #12830 MR 0454581 (56:12830)
  • [33] N. C. Yannelis, The core of an economy with differential information, Econom. Theory 1 (1991), 183-197. MR 1102549 (92b:90050)
  • [34] A. C. Zaanen, Riesz spaces, II, North-Holland, Amsterdam and New York, 1983. MR 86b:46001 MR 704021 (86b:46001)

Review Information:

Reviewer: C. D. Aliprantis
Journal: Bull. Amer. Math. Soc. 28 (1993), 190-194
DOI: https://doi.org/10.1090/S0273-0979-1993-00353-7
American Mathematical Society