Download PDF - Topological conditions for bound-2 isomorphisms of C(X)All rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

Topological conditions for bound-2 isomorphisms of C(X)

Authors 1, 2

Affiliations

  1. Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, U.S.A.
  2. Goldsmiths' College, University of London, London SE14, England

Abstract

We establish the topological relationship between compact Hausdorff spaces X and Y equivalent to the existence of a bound-2 isomorphism of the sup norm Banach spaces C(X) and C(Y).

Bibliography

  1. D. Amir, On isomorphisms of continuous function spaces, Israel J. Math. 3 (1965), 205-210.
  2. E. Behrends, M-structure and the Banach-Stone Theorem, Lecture Notes in Math. 736, Springer, 1979.
  3. Y. Benyamini, Near isometries in the class of L1-preduals, Israel J. Math. 20 (1975), 275-291.
  4. M. Cambern, A generalized Banach-Stone Theorem, Proc. Amer. Math. Soc. 17 (1966), 396-400.
  5. M. Cambern, On isomorphisms with small bounds, ibid. 18 (1967), 1062-1066.
  6. M. Cambern, On L1 isomorphisms, ibid. 78 (1980), 227-229.
  7. M. Cambern, Isomorphisms of spaces of norm continuous functions, Pacific J. Math. 116 (1985), 243-254.
  8. M. Cambern and P. Greim, The bidual of C(X,E), Proc. Amer. Math. Soc. 85 (1982), 53-583.
  9. M. Cambern and P. Greim, The dual of a space of vector measures, Math. Z. 180 (1982), 373-378.
  10. H. B. Cohen, A bound-two isomorphism for C(X) Banach spaces, Proc. Amer. Math. Soc. 50 (1975), 215-217.
  11. H. B. Cohen, A second-dual method for C(X) isomorphism, J. Funct. Anal. 23 (1975), 107-118.
  12. C. H. Chu and H. B. Cohen, Isomorphisms of spaces of continuous affine functions, Pacific J. Math. 155 (1992), 71-85.
  13. J. Dixmier, Sur certains espaces considérés par M. H. Stone, Summa Brasil. Math. 2, (1951), 151-182.
  14. H. Gordon, The maximal ideal space of a ring of measurable functions, Amer. J. Math. 88 (1966), 827-843.
  15. J. R. Isbell and Z. Semadeni, Projection constants and spaces of continuous functions, Trans. Amer. Math. Soc. 107 (1963), 38-43.
  16. K. Jarosz, Small isomorphisms of C(X,E) spaces, Pacific J. Math. 138 (1989), 295-315.
  17. S. Kakutani, Concrete representation of abstract (L)-spaces and the mean ergodic theorem, Ann. of Math. 42 (1941), 523-537.
  18. J. L. Kelley, Banach spaces with the extension property, Trans. Amer. Math. Soc. 72 (1952), 323-326.
  19. J. Lamperti, On the isometries of certain function spaces, Pacific J. Math. 8 (1958), 459-466.
Studia Mathematica
1995/113/1
Export to PBN, Opens in new tab
Pages:
1-24
Main language of publication
English
Received
1992-11-20
Accepted
1993-10-25
Published
1995
Exact and natural sciences