Israel Journal of Mathematics

, Volume 209, Issue 1, pp 1–13 | Cite as

On isomorphisms of Banach spaces of continuous functions



We prove that if K and L are compact spaces and C(K) and C(L) are isomorphic as Banach spaces, then K has a π-base consisting of open sets U such that Ū is a continuous image of some compact subspace of L. This sheds new light on isomorphic classes of spaces of the form \(C({[0,1]^\kappa })\) and spaces C(K) where K is Corson compact.


Banach Space Compact Space Continuous Image Nonempty Open Subset Isomorphic Embedding 
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  1. [1]
    F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Graduate Texts in Mathematics, Vol. 233, Springer, New York, 2006.Google Scholar
  2. [2]
    D. Amir, On isomorphis of continuous function spaces, Israel Journal of Mathematics 3 (1965), 205–210.MathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    S. Argyros, S. Mercourakis and S. Negrepontis, Functional analytic properties of Corsoncompact spaces, Studia Mathematica 89 (1988), 197–228.MathSciNetMATHGoogle Scholar
  4. [4]
    Y. Benyamini, Small into-isomorphisms between spaces of continuous functions, Proceedings of the American Mathematical Society 83 (1981), 479–485.MathSciNetCrossRefMATHGoogle Scholar
  5. [5]
    Cz. Bessaga and A. Pełczyński, Spaces of continuous functions. IV (On isomorhic classification of C(S) spaces), Studia Mathematica 19 (1960), 53–62.MathSciNetMATHGoogle Scholar
  6. [6]
    M. Cambern, On isomorphisms with small bounds, Proceedings of the American Mathematical Society 18 (1967), 1062–1066.MathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    E. Medina Galego, On isomorphic classification of C(2 m ⊕ [0, α]), Fundamenta Mathematicae 204 (2009), 87–95.MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    K. Jarosz, Into isomorphisms of spaces of continuous functions, Proceedings of the American Mathematicasl Society 90 (1984), 373–377.MathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    O. Kalenda, Valdivia compact spaces in topology and Banach space theory, Extracta Mathematicae 15 (2000), 1–85.MathSciNetMATHGoogle Scholar
  10. [10]
    P. Koszmider, The interplay between compact spaces and the Banch spaces of their continuous functions, in Open Problems in Topology II, Elsevier, Amsterdam, 2007.Google Scholar
  11. [11]
    W. Marciszewski and G. Plebanek, On Corson compacta and embeddings of C(K) spaces, Proceedings of the American Mathematical Society 138 (2010), 4281–4289.MathSciNetCrossRefMATHGoogle Scholar
  12. [12]
    A. A. Miljutin, Isomorphisms of the spaces of continuous functions over compact sets of the cardinality of the continuum, Har’ kovskiĭ Ordena Trudovogo Krasnogo Znameni Gosudarstvennyĭ Universitet im. A. M. Gor’kogo. Teorija Funkciĭ, Funkcional’nyĭ Analiz i ih Priloženija 2 (1966), 150–156 (Russian).MathSciNetMATHGoogle Scholar
  13. [13]
    S. Negrepontis, Banach spaces and topology, in Handbook of Set-theoretic Topology, K. Kunen, J.E. Vaughan (edts.), North-Holland, Amsterdam 1984, pp. 1045–1142.CrossRefGoogle Scholar
  14. [14]
    O. Okunev, Fréchet property in compact spaces is not preserved by M-equivalence, Commentationes Mathematicae Univesitatis Carolinae 46 (2005), 747–749.MathSciNetMATHGoogle Scholar
  15. [15]
    A. Pełczyński, Linear extensions, linear averagins and their applications to linear topological characterizations of spaces of continuous functions, Dissertationes Mathematicae 58 (1968).Google Scholar
  16. [16]
    G. Plebanek, On positive embeddings of C(K) spaces, Studia Mathematica 216 (2013), 179–192.MathSciNetCrossRefMATHGoogle Scholar
  17. [17]
    Z. Semadeni, Banach Spaces of Continuous Functions, Monografie Matematyczne, Tom 55, PWN-Polish Scientific Publishers, Warsaw, 1971.Google Scholar

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© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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