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On the primariness of the Banach space $ l\sb {\infty}/C\sb 0$


Authors: Lech Drewnowski and James W. Roberts
Journal: Proc. Amer. Math. Soc. 112 (1991), 949-957
MSC: Primary 46B20; Secondary 46B25
DOI: https://doi.org/10.1090/S0002-9939-1991-1004417-0
MathSciNet review: 1004417
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Abstract | References | Similar Articles | Additional Information

Abstract: In a response to a question asked by Leonard and Whitfield (1983) we show that, under the Continuum Hypothesis, the Banach space $ {l_\infty }/{C_0}$ is primary.


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

  • [1] Y. Benyamini, An $ M$-space which is not isomorphic to a $ C(K)$ space, Israel J. Math. 28 (1977), 98-102. MR 0458145 (56:16348)
  • [2] P. G. Casazza, Finite dimensional decompositions in Banach spaces, Contemp. Math. 52 (1986), 1-31. MR 840692 (87h:46036)
  • [3] J. Deistel and J. J. Uhl, Jr., Vector measures, Math. Surveys 15 (1977). MR 0453964 (56:12216)
  • [4] A. Dow, Saturated Boolean algebras and their Stone spaces, Topology Appl. 21 (1985), 193-207. MR 813288 (87d:54050)
  • [5] L. Drewnowski and J. W. Roberts, On Banach spaces containing a copy of $ {l_\infty }$, and some three-space properties (to appear).
  • [6] I. E. Leonard and J. H. M. Whitfield, A classical Banach space: $ {l_\infty }/{c_0}$, Rocky Mountain J. Math. 13 (1983), 531-539. MR 715776 (84j:46030)
  • [7] J. Lindenstrauss, On complemented subspaces of $ m$, Israel J. Math. 5 (1967), 153-156. MR 0222616 (36:5666)
  • [8] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces I. Sequence spaces, Springer-Verlag, Berlin, 1977. MR 0500056 (58:17766)
  • [9] J. van Mill, An introduction to $ \beta \omega $, Handbook of set-theoretic topology (K. Kunen and J. E. Vaughn, eds.), North-Holland, Amsterdam, 1984, pp. 503-567. MR 776630 (86f:54027)
  • [10] S. Negrepontis, The Stone space of the saturated Boolean algebras, Trans. Amer. Math. Soc. 141 (1969), 515-527. MR 0248057 (40:1311)
  • [11] J. R. Partington, Subspaces of certain Banach sequence spaces, Bull. London Math. Soc. 13 (1981), 162-166. MR 608103 (82h:46036)
  • [12] H. P. Rosenthal, On relatively disjoint families of measures, with some applications to Banach space theory, Studia Math. 37 (1970), 13-36. MR 0270122 (42:5015)
  • [13] E. Saab and P. Saab, On the Banach space $ {X^{**}}/X$, Bull. Sci. Math. (2) 107 (1983), 139-144. MR 704721 (84f:46024)
  • [14] R. C Walker, The Stone-Cech compactification, Springer-Verlag, New York, 1974. MR 0380698 (52:1595)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1004417-0
Keywords: Primary Banach space, Stone-Cech compactification of the integers, continuum hypothesis
Article copyright: © Copyright 1991 American Mathematical Society

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