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2016 | 36 | 1 | 33-43
Tytuł artykułu

On some properties of quotients of homogeneous C(K) spaces

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EN
Abstrakty
EN
We say that an infinite, zero dimensional, compact Hausdorff space K has property (*) if for every nonempty open subset U of K there exists an open and closed subset V of U which is homeomorphic to K. We show that if K is a compact Hausdorff space with property (*) and X is a Banach space which contains a subspace isomorphic to the space C(K) of all scalar (real or complex) continuous functions on K and Y is a closed linear subspace of X which does not contain any subspace isomorphic to the space C([0,1]), then the quotient space X/Y contains a subspace isomorphic to the space C(K).
Twórcy
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, ul. Umultowska 87, 61-614 Poznań, Poland
Bibliografia
  • [1] H.H. Corson, The weak topology of a Banach space, Trans. Amer. Math. Soc. 101 (1961), 1-15. doi: 10.1090/S0002-9947-1961-0132375-5
  • [2] R. Engelking, General Topology (Monografie Matematyczne 60, PWN - Polish Scientific Publishers, Warszawa, 1977).
  • [3] L. Gillman and M. Jerison, Rings of Continuous Functions (D. Van Nostrand Company, INC. Princeton, N.J.-Toronto-New York-London, 1960).
  • [4] J.L. Kelley, General Topology (D. Van Nostrand Company, Inc., Toronto-New YorkLondon, 1955).
  • [5] J. Lindenstrauss and A. Pełczyński, Contributions to the theory of the classical Banach spaces, J. Funct. Anal. 8 (1971), 225-249. doi: 10.1016/0022-1236(71)90011-5
  • [6] A. Michalak, On monotonic functions from the unit interval into a Banach space with uncountable sets of points of discontinuity, Studia Math. 155 (2003), 171-182. doi: 10.4064/sm155-2-6
  • [7] A. Michalak, On uncomplemented isometric copies of c0 in spaces of continuous functions on products of the two-arrows space, Indagationes Math. 26 (2015), 162-173. doi: 10.1016/j.indag.2014.09.003
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1180
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